SSC Physics by Enoch Reddy

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Physics SSC Gnan Mantra

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Chapter-1 MEASUREM ENT OF LENGTH

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Archimedes

Archimedes: Mathematician Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Born: 287 BC, Syracuse, Italy Full name: Archimedes of Syracuse Nationality: Greek Assassinated: 212 BC, Syracuse, Italy Parents: Phidias

ARCHIMEDES' SCREW One such story recounts how a perplexed King Hiero was unable to empty rainwater from the hull of one of his ships. The King called upon Archimedes for assistance. Archimedes' solution was to create a machine consisting of a hollow tube containing a spiral that could be turned by a handle at one end. When the lower end of the tube was placed into the hull and the handle turned, water was carried up the tube and out of the boat. The Archimedes Screw is still used as a method of irrigation in developing countries.

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THE "EUREKA" STORY ILLUSTRATED BY KEVIN KALLAUGHER.

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MEASUREMENT OF LENGTH

IMPORTANT POINTS 

Screw gauge works on the principle of a screw in a nut.

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Pitch of the screw is the distance advanced by the tip of the screw for one complete revolution of the head.

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The distance between two adjacent threads is also called the pitch of the screw.

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Least count of the screw gauge:

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Thickness of a wire = P.S.R. + H.S.R. x L.C.

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Two types of zero errors 1) Positive zero error 2) Negative zero error.

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PREVIOUS PUBLIC EXAMINATIONS QUESTIONS 1. How do you determine the diameter of wire using a Screw gauge? (June 2006, March ‘09, 03) 2. What is the principle of a Screw gauge? (June 2002, March 2000) 3. Define the least count of a Screw gauge. (March 2001) 4. Draw a neat sketch of Screw gauge and label the parts. (March ‘12, ‘07, ‘05, ‘01, Apr ‘08, Jun‘08) 5. What are positive and negative zero errors of a screw gauge? How are they determined? (June 2010, Oct. 1999) 6. Draw the diagrams showing zero errors of a screw gauge. A) No zero error B) Negative zero error C) Positive zero error. (Mar 11, 10, Jun 07) 7. What is the instrument you use in the laboratory to find out the thickness of a glass plate? 8. Draw a neat diagram and label its parts. (March 2008)

Short Answer Questions 1. What is the pitch of a screw? (T.Q.) A. The distance between two adjacent threads or the distance travelled by the tip of the screw In one complete revolution of the head is called the pitch of the screw.

2. What is the least count of a screw gauge? (T.Q.) A. When the head of the screw gauge is rotated so that only one head scale division crosses the reference or Index line then the distance moved by the tip of the screw is called the least count of the screw gauge.

Very Short Answer Questions 1. What is the principle of a screw gauge? (T.Q.) (June 2002, March 2000) A. Screw gauge works on the principle of a screw in a nut. 2. Mention the uses of screw gauge. A. A screw gauge is used to measure the thickness of a thin glass plate and the diameter. of a thin wire or a small sphere. 3. What is meant by zero error of a screw gauge? A. If the zeroth division of the head scale does not coincide with the index line of the Pitch Scale then the screw gauge is said to have zero error.

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Long Answer Questions 1. Give the description of a screw Gauge? T.Q. Description: Parts: 1) F :U-shaped metallic frame 2) C Hollow cylinder 3) P Pitch scale 4) S1: Flat shaft 5) S2: Flat tip 6) M: Milled head 7) B : Jacket barrel 8) H : Head scale 9)Sâ&#x20AC;&#x2122; : Screw 1) A screw gauge consists of a U - shaped metallic frame F. 2) A flat shaft S1, (Stud) is fixed to one end of this frame. 3) A hollow long cylinder C is fixed on the opposite end of this frame. 4) This hollow cylinder has fine threads cut inside it. It serves as the nut. 5) A line parallel to the axis of this hollow cylinder is drawn on its outer surface called the index line is divided into some equal divisions. This is the Pitch Scale (P). 6) A screw with a flat tip S2 having threads exactly identical to the threads â&#x20AC;&#x2DC;cut inside tb cylinder, moves through the cylinder C. 7) To the other end of the screw, a milled head M is connected. 8) To this milled head, one end of a barrel B (another hollow cylinder) connected. This barrel B forms a jacket to the first hollow cylinder C. 9) The other end of the barrel is tapered and has 100 or 50 equal divisions on it. This is called the head scale (H). 2. How do you determine the diameter of a wire using a screw gauge? (T.Q.) (June 2006, March 09, 2003) 1) To determine the diameter of a wire by using screw gauge, first we should find the least count of the screw gauge.

) The zero error of the screw gauge if any is noted. 3) The wire is placed between the shafts S and S2 and the head scale is rotated anti- clockwise so that

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the shafts hold the wire tightly. 4) The value of the pitch scale division which just precedes edge of the head scale is noted as Pitch Scale Reading (P.S.R.). 5) The value of the head scale division which just coincides with the index line is the observed Head Scale Reading (H.S.R.). 6) Diameter of the wire = P.S.R. + H.S.R. x L.C. 7) The wire is placed at different positions in between the studs and the observations are recorded. 3. What are positive and negative zero errors of a screw gauge? How are they determined? (T.Q.) (Oct. ‘99) A. There are two types of zero errors depending on whether the zeroth division of the head scale is below or above the index line. They are 1) Positive zero error, 2) Negative zero error.

Positive zero error: If the zeroth division of the head scale is below the index line of the pitch scale by n divisions, the error is said to be positive and the correction is negative. Let ‘n’ be the particular division of head scale division that coincides with the index line. Then the corrected head scale reading will be C.H.S.R. = Observed (H.S.R.) — n.

Negative zero error: If the zeroth division of the head scale is above the index line the error is said to be negative and the correction is positive Let n be the particular division of the head scale negative zero error division that coincides with the index line. Then the corrected head scale reading C.H.S.R. = Observed (H.S.R.) + n. PROBLEMS 1. The head of a screw gauge is divided into 50 divisions. It advances 1 mm when screw is turned through 2 rotations. Find the pitch of the screw and least count of the screw gauge. (T.Q.)

Solution: 1) Given : No. of head scale divisions (N) = 50 2) Pitch of the screw (P)

2. When the above screw gauge is used to measure the diameter of a nail, the pitch scale reading is found to be 1.5 mm and the head scale reading is 18. Find the diameter of the nail.(T.Q.)

Solution: 1) Given : RS.R. = 1.5 mm; H.S.R. = 18

www.gnanmantra.com L.C. = 0.01 mm 2) Formula : Diameter P.S.R. + H.S.R. x L.C. 3)

Diameter = 1. 5 + 18 x .01 = 1.5÷ .18 = 1.68mm

3. Find the least count of a screw gauge whose head scale is divided into 200 divisions, if it moves 5 mm distance when the head is rotated through 5 revolutions. (T.Q.) Solution: 1) Given No. of revolutions (N) = 200 Distance travelled by the screw x = 5 mm No. of revolutions n=5

2) But Pitch of the screw P=

4. While measuring the diameter of a lead shot using a screw gauge, the reading on the pitch scale is found to be 7.5 mm and that on the head scale is 48. If the least count is 0.01 mm and zero error is + 0.05 mm, find the diameter of the lead shot. (T.Q.) Sol. 1) Given : P.S.R. = 7.5 mm, H.S.R. = 48 L.C. = 0.01 mm, Zero error = ÷ 0.05 mm Zero correction = — 0.05 mm 2) Formula Diameter of the lead shot = P.S.R. + H.S.R. x L.C. ± Correction 3) Diameter = 7.5 + 48 x0.01 —0.05 mm = 7.5 + 0.48—0.05 = 7.98—0.05 = 7.93 mm Diagrams 1. Draw a neat diagram of screw gauge and label its parts. (or) What is the instrument you use in the laboratory to find out the thickness of a glass plate? Draw a neat diagram and label its parts. (March ‘I2, ‘08, ‘07, ‘05, ‘0 1, April, ‘08, June ‘ 12, ‘10, O8 04) Parts: 2) F :U-shaped metallic frame 2) C Hollow cylinder 3) P Pitch scale 4) S1: Flat shaft 5) S2: Flat tip 6) M: Milled head 7) B : Jacket barrel 8) H : Head scale 9)S’ : Screw

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2. Draw the diagrams showing zero errors of a screw gauge. (March ‘13, ‘11, ‘10, June ‘07)

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Chapter-2 OUR UNIVERSE:

GRAVITATION

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Introduction: The universe can be defined as all matter and energy includes the earth , the solar system , the galaxies, and contents of huge space , regarded as whole. Where earth is a part of our universe, there we are going to learn about the earth briefly and about its gravitation force any other types of force. Which influences on the earth. We all know earth is a huge mass with all the godly power in such powers gravitational force is one of the important fact of the history. We all know the law of gravitation was first introduced by Sir ISSAC NEWTON who found it eventually. When he was sitting under apple tree. We all know earth is a huge mass ball which has huge rocks on the surface and huge water bodies. But it is experimentally proved that anybody of perfect spherically shape of uniform magnitude of all points on its surface, always pointing directly towards the sphere center, where the earth also posses the same force but slightly events in the both magnitude and direction. Its force is influenced.

HISTORY: In 4th century BC. Aristotle believed that no motion will be produced simply without any cause, the cause of downward motion of heavy bodies towards the earth was related to nature thus according to Aristotle heavy bodies are not attracted to earth by an external force of gravity but it does internally due to gravity in the earthâ&#x20AC;&#x2122;s core. In the 7th century the Indian Mathematician Brahmagupta stated that bodies fall toward the earth as it in nature of earth to attract bodies as just it is in the nature of water to flow. Earthâ&#x20AC;&#x2122;s gravity was described by Bhaskarachariya, the great Indian Mathematician in the 11th century in his books called Siddhantha Shiromani.

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During 17th century, Galileo found that all objects falling down toward the earth accelerates equally when he took two different weights and threw it from the tower of pizza. In 1687 English Mathematician Sir Isaac Newton Published the inverse square law of gravitation, Newton’s theory enjoyed its success of understanding the term gravitation. All knew that gravitation has invented by whom and how, when one fine day Sir Isaac Newton was lying under an apple tree found the ripen falling down he was shocked to see that why its falling down why not up this lead to Motion of Laws of Gravitation force by Newton.

SIR ISSAC NEWTON

Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727) was an English physicist and mathematician who is widely regarded as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations for most of classical mechanics. Newton also made seminal contributions to optics and shares credit with Gottfried Leibniz for the invention of the infinitesimal calculus. Newton's Principia formulated the laws of motion and universal gravitation that dominated scientists' view of the physical universe for the next three centuries. It also demonstrated that the motion of objects on the Earth and that of celestial bodies could be described by the same principles. By deriving Kepler's laws of planetary motion from his mathematical description of gravity, Newton removed the last doubts about the validity of the heliocentric model of the cosmos. Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 at Woolsthorpe Manor in Woolsthorpe-byColster worth, a hamlet in the county of Lincolnshire. He was born three months

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after the death of his father, a prosperous farmer also named Isaac Newton. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug from the age of about twelve until he was seventeen, Newton was educated at The King's School, Grantham. He was removed from school, and by October 1659, he was to be found at Woolsthorpeby-Colsterworth,Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge as a sizar â&#x20AC;&#x201C; a sort of work-study role.[13] At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers, such as Descartes, and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became infinitesimal calculus In 1679, Newton returned to his work on (celestial) mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679â&#x20AC;&#x201C;80 with Hooke, After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about 9 sheets which was copied into the Royal Society's Register Book in December 1684.[47] This tract contained the nucleus that Newton developed and expanded to form the Principia. The Principia was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that enabled many of the advances of the Industrial Revolution which soon followed and were not to be improved upon for more than 200 years, and are still the underpinnings of the non-relativistic technologies of the modern world. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. Newton died in his sleep in London on 20 March 1727 (OS 20 March 1726; NS 31 March 1727)[1] and was buried in Westminster Abbey. Voltaire was present at his funeral and praised the British for honoring a scientist of heretical religious beliefs with burial there. A bachelor, he had divested much of his estate to relatives during

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his last years, and died intestate. After his death, Newton's hair was examined and found to contain mercury, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life

SCOPE AND APPLICATION: NEWTONS 1st LAW MOTION A body tends to be in an stable position until and unless a force acts on it .” USES IN DAILY LIFE  We also tends to be at an single place idle until and unless our brain pushes us to walk or move.  A bike or a car remains in its stable position until and unless the acceleration is increased.  A auto rickshaw or a bicycle only moves when the person tries to paddle or push from the back.  When a car moves the rest of the body parts and the passengers tends to be in its same position. This effect is called as inertia  Blood rushes from your fore head to feet while quickly stopping when riding or a descending elevator  The head of the hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.  Head rests are placed in cars to prevent whiplash injuries during rear end collision. NEWTON’S 2nd LAW OF MOTION : “ states that the force applied on a body is equal tp product of mass of body and acceleration produced”.  It is applied all over in the first newton law of motion NEWTON’S 3rd LAW MOTION “It says that every action has a equal and opposite reactionin opposite direction “. let us see some examples  A rocket tends to go up when it exerts pressure downwards.

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 A simple example of getting up out of chair. To get up one must push down the chair so that the reaction will help one standup.  To walk one pushes his|her feet on the ground to move forward.  In the pistons and cylinders engine of car or a truck works in the same way using third law of newton’s BASIC CONCEPTS : This chapter is totally based on the Newton’s law of motion and his gravitational law so let us look into the basics of Newton’s principle and his law on motion Newton’s 1st LAW MOTION

“It states that everybody tends to be in its stable or uniform position until and unless it exreted by and external force”. Newton’s 2nd LAW OF MOTION :

“ It states that force exerted on a body is equal to the product of their mass and acceleration” Newton’s 3rd LAW MOTION:

“ It states that forevery action there is an equal and opposite reaction in opposite direction “ NEWTONS LAW OF UNIVERSAL GRAVITATION :

STATEMENT : Everybody in the universe attracts every otherbody with a force which is directly propotional to the product f their masses and inversely propotional to the square of their distance between them . the force act along the line joining the two bodies The expression given for the above statement is as follows

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 G = F r2 M1 m2 ACCELERATION DUE TO GRAVITY: The uniform acceleration produce by a freely fallig body due to gravitational pull of the earth is knowna sa acceleration due to gravity Calculation of acceleration due gravity : if a stone fo mass m is droppe from distance r from the center of the earth whose mass Mthe the force exerted by the earth on the stone is given by F= G M r2 The force produces acceleration g in it So by second law of newtons F= m x a i.e mass x acceleration Here we refer acceleration a =g Then F= mg From equation(3) and (4) We get mg = G Mm/r2  g = GM r2 There for we can conclude thet ‘g’ is independent fo their mass of the stone .

BIOGRAPHY OF SIR ISAAC NEWTON Name Occupation

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Birth date Death date Education . Place of birth Place of death

: : : : :

SIR ISAAC NEWTON Philosopher, Mathematician,Astronomer, Physicist January 04, 1643 MARCH 31, 1727 The King's School, University of Cambridge, Trinity College Woolsthorpe, Lincolnshire, England, UK London, England, UK.

BEST KNOWN FOR English, physicist and mathematician Sir Isaac Newton, most famous for his law of gravitation, was instrumental in the scientific revolution of the 17th century.

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Some of the Quotes 1. "I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then in finding a smoother pebble or prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me." 2. "Plato is my friend, Aristotle is my friend, but my greatest friend is truth." 3. "It is the perfection of God's works that they are all done with the greatest simplicity." â&#x20AC;&#x201C; Isaac Newton

What Really Happened with the Apple? Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "acceleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree.

Sir Isaac's Most Excellent Idea Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth.

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IMPORTANT POINTS  According to Ptolemaic solar system, earth is at the centre of the universe and is stationary.  In Copernican solar system, the earth rotates round its own axis. Further the earth revolves round the sun i a circular orbit.  Copernican theory states that all the planets in the solar system rotate about their axes and revolve round the sun in different circular orbits.  According to Newton’s Law of gravitation

 The acceleration produced in a freely falling body due to gravitational pull of the earth is called acceleration due to gravity. 

Acceleration due to gravity (g) is inversely proportional to the square of the distance of the body from the centre of the earth.

 The value of acceleration due to gravity (g) is maximum at the poles and minimum at the equator.  g’ decreases as we go upwards or downwards (inwards) from the surface of earth.  Hooke’s law gives the relation between the extension in length of a spring and the force acting’on it.  Hooke’s law is useful in determining the weight of a body.  Weight of a body W = mg.

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Questions From Previous Exams 1. What is acceleration due to gravity? (March 10, 06, April 2008) 2. Differentiate between mass and weight of a body. (Mar ‘12, Jun 2006, 2004) 3. State Hooke’s Law. (March 2004) 4. State the Newton’s Law of Universal gravitation. Calculate the gravitational force on an object of mass 10 kg. (March 2003, 2000) 5. The weight of a body is not the same on the surface of the earth at all places. Specify the reason. (June 2002) 6. Derive the relation between acceleration due to gravity and universal gravitational constant (Jun 01) (Mar 99) (Mar 05) (Mar 07,08) (Jun 08) (Jun 08) 7. Why is the weight of a body not the same at poles and at the equator? 8. What is Heliocentric theory? 9. Define the weight of a body. 10. Why does the value of ‘g’ decrease when we go deep into the earth? 11. What are the factors that influence the value of ‘g’. 12. Define the mass of a body.

Short Answer Type Questions 1. What are the factors that influence the value of ‘g’? (June 2008) (T.Q) A. Factors that influence the value of ‘g’ are A) Shape of the earth a) at pole and b) at the equator B) Altitude C) Depth and D) Local conditions. 3. Distinguish between Gravitational constant (G) and acceleration due to gravity.

4. How does acceleration due to gravity varies with height and depth? A. Height: As we move upwards from the surface of the earth, the distance from the centre f the earth increases. Hence ‘g’ value decreases. Acceleration due to gravity at height ‘h’ is

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Where ‘r’ is the radius of the earth. Depth: As we go deep inside the earth ‘g’ value decreases due to the decrease of effective mass of the earth. Acceleration due to gravity at a depth ‘d’ is given by of the earth.

where ‘r’ is the radius

Very Short Answer Questions 1. What is Geocentric theory? (T.Q.) A. According to geocentric theory, the earth is stationary and is at the centre of the universe, with the sun, the moon, planets and stars revolving around the earth. 2. What is Heliocentric theory? (T.Q.) (March 2005) A. According to heliocentric theory, the earth and the other planets move in perfect circles around the sun located at the centre of these circles. 3. What is acceleration due to gravity? (T.Q.) (March 2010, 2006, April 2008) A. The uniform acceleration produced in a freely falling body due to gravitational pull of the earth is known as acceleration clue to gravity ‘g’. 4. Define the mass of a body (T.Q.) (June 2008) A. The mass (m) of the body is the quantity of matter contained in it and its value is the same any- where in the universe. 5. Define the weight of a body. (T.Q.) (March 2011, 2007) A. The weight (mg) of a body is the force with which it is attracted by the earth towards its centre. (W = mg) 6. State Hooke’s law. (T.Q.) (June ‘10, ‘07, March 2004) A. Hooke’s law: Hooke’s law states that within the elastic limit of the spring, the stretching of the spring is proportional to the applied force. (Or) Hooke’s law states that within the elastic limit, stress is directly proportional to the strain. 7. Why is the weight of a body not the same at the poles and at the equator? - (March 1999) A. 1) The weight of a body is W = mg. It means the weight of a body depends upon ‘g’ (acceleration due to gravity). 2) As the value of g is maximum at the poles and minimum at the equator the weight of the body is not the same at the poles and at the equator.

www.gnanmantra.com 8. “The weight of the body is not the same on the surface of the earth at all places”. Specify the reason. (June 2002) A. 1) The weight of a body is W = mg. It means the weight of a body depends upon g’ (acceleration due to gravity). 2) As the value of ‘g’ is not the same on the surface of the earth at all places the weight of a body is not the same at all places on the surface of the earth. 9. Why does the value of ‘g’ decrease as we go deep inside a mine (or the earth)? (March ‘13, ‘08) A. As we go deep inside mine (or the earth) the effective mass of the earth decreases. So the value of ‘g’ decreases. 10. Define universal gravitational constant ‘G’. A. The gravitational constant (G) is equal to the force of attraction between two unit masses when they are unit distance a parts. 11. What is gravitymeter? Give two examples. A. The sensitive instrument used to measure the small changes in the value of ‘g’ at a given location is called gravity meter. Eg: - Gulf gravitymeter and Boliden gravitymeter. 12. The value of ‘g’ is minimum at the equator. Give the reason. A. 1) We know that g where r is the radius of the earth. 2) The radius of the earth is maximum at the equator due to bulging of the earth. 3) So the value of ‘g’ is minimum at the equator. 13. Why is the value of ‘g’ maximum at the poles of the earth? A. 1) We know that where ‘r’ is the radius of the earth. 2) The radius of the earth is minimum due to flattening of the earth at the poles. 3) So the value of ‘g’ is maximum at the poles. 14. Why do bodies lying on the earth not collide with each other, though gravitational force of attraction acts between them? A. The gravitational force of attraction between any two bodies on earth is negligible. The attraction between the earth and any such body is considerable. So bodies lying on the earth do not collide.

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Long Answer Type Questions

2. Differentiate between Mass and Weight of a body. (T.Q.) (March ‘12, June ‘06, ‘04, ‘03)

a) Write Newton’s Law of Universal gravitation. b) Calculate the gravitational force on an object of mass 10 kg. (March 2003, 2000) A. a) Newton’s Law of Universal gravitation: Everybody in the universe attracts any other body with a force (F) which is directly proportional to the product of their masses (m1, m2) and is inversely proportional to the square of the distance (r2) between them.

www.gnanmantra.com 3. Derive the relation between acceleration due to gravity and gravitational constant (T.Q.) (June 2001) A. Relation between ‘g and ‘G’: 1) If a stone of mass m is dropped from a distance r from the centre of the earth of mass M, then the force exerted by the earth on the stone is given by the Universal law of gravitation as: -

This force produces acceleration g in the body. 2) We also know from Newton’s second law of motion that Force = mass x acceleration F=ma=mg (2) 3) From equations (1) and (2),

4) This relation shows that ‘g’ is independent of the value of the mass (m) of the stone (body). 4. You know that the gravitational attraction of the earth on any object is proportional to its mass. Thus why do heavy objects not fall faster than light objects? (T.Q.) A. 1) Gravitational attraction of the earth on any object is proportional to its mass (m).

2) But the acceleration due to gravity of the earth is r is the radius of the earth.

where M is the mass of the earth and

3) It means ‘g’ is independent of the mass of the body. 4) Hence all bodies fall on the earth with the same acceleration whatever may be their mass. 5. Describe an experiment to determine the weight of a body. (or) Describe an experiment to prove Hooke’s Law. (T.Q.) A. Experiment: Aim: To determine the weight of a body. Apparatus required: 1) An extensible spring. 2) Pan 3) Pin 4) Weights 5) Retort stand 6) Metre scale 7) Plasticine. Procedure:

www.gnanmantra.com 1) Suspend the extensible spring from a suitable stand with a hook and attach a pan to the lower end of the spring. 2) Also fix a pin at the lower end and at right angles to the spring by means of a little plasticine. The horizontal pin serves as a pointer. 3) Fix the metre scale vertically so that the pin (pointer) can move over the scale which serves as a spring balance. 4) Record the reading of the pointer on the scale (l0) initially. Now add 10 gram weight to the scale pan. Note the reading of the pointer (l1). Spring Balance

Parts: 1) Spring 2) Scale 3) Pan 4) Pointer 5) Stand 5) Proceed like this, increasing loads regularly in steps of 10 grams upto about 100 grams. Record the values of fl in each case. 6) Take a second set of readings while the pan is gradually unloaded in the same regular steps. Enter the readings (1.) in the table; 7) Plot a graph between stretching of the spring (l-l0) against force (f). Put the body (whose weight is to be found) on the pan and note the extension (I — l0). 8) The value of [corresponding to (l — l0) is found out from the graph. This value of f is the weight of the body. 9) It is clear from the table that

is constant.

It means the extension in the spring is proportional to the applied force which is Hooke’s Law.

6. State the Newtons Law of Universal gravitation and derive (June 2001, March 2003, 2000) A. Newton’s Universal law of gravitation: Everybody in the universe attracts every other body with a force (F) which is directly proportional to the product of their masses (m1 m2) and inversely proportional to the square of the distance

between them. The force acts along the line joining the two bodies.

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Derivation of 1) Let the two bodies of masses m1 and m2 separated by a distance of ‘r’ and the force of attraction between them be ‘F. 2) According to the law, the force (F) of attraction between two bodies is directly proportional to the product of their masses (m1 m2). 3) Also the force of attraction between two bodies is inversely proportional to the square of the distance

4) From equations (1) & (2)

where ‘G is Proportionality constant called universal gravitational constant. 7. What are the factors that influence the value of ‘g’? Give details. (T.Q.) A. The factors that influence the value of g’ is given in detail.

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Chapter-3 KINEMATICS

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INTRODUCTION: Physics in kinematics deals with the position and motion that possessed by a moving or a stable body. To be simple we can say that kinematics is a branch of physics that deals with the study of motion . i.e where you are and what would be your destination regardless of direction. For eg: If you start from your home and your destination is your school . the distance is 5km so what will be your motion Is it uniform , accelerating or stable, speed ,velocity harvested which way the rate changes, acceleration flow fasten speed up, slowdown or change direction the rate at which velocity charges.how fast you will be . these all matter in the field of kinematics. SCALAR QUANTITY : A scalar quantity is a measurement that has one magnitude , mass obtain , speed energy and time. VECTOR QUANTITY A vector quantity is a measurement that has a magnitude and direction, position ,velocity, accerlation force. HISTORY : The history of kinematics , the story of the development of the geometry of motion is composed of evolvements in machines, mechanism and mathematician . in the period of invention and kinematics there was no unity nor plan. Physical problems were actually appeared to the algebraic speculations, the concept of kinematics a science was affirmed and the ancient art of mechanism complemented more significantly it is the ability to some a wide variety of problems. The theory of kinematics states in year 19th century and the theory of machine as seen through the contribution of german scientist. Franz Reuleaux(1829-1905) often called as father of kinematics. Machines mechanics are largely hidden in modern technology and virtually absent from general mechanical emergency education. The centre of density a mechanism of machine is kinematics, a subject that a half century ago as a part of dynamics, Mechanism of design of todayâ&#x20AC;&#x2122;s engineering has been large. But in 17th century has a different vision for revolution in engineering. Franz Revlance of

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Berlin was the first generation engineering who have advocated a mathematical treatment of mechanical engineering within the context of machines. Many of our ideas about kinematics of mechanics and multi body system original in this period and show from Revleaux’s two major book, the kinematics of machinery(18751870), the constructor, a machine design book which went through four edition in four language. FRANZ REULEAUX EARLY LIFE: Franz Reuleaux (September 30, 1829 – August 20, 1905), was a mechanical engineer and a lecturer of the Berlin Royal Technical Academy, later appointed as the President of the Academy. He was often called the father of Kinematics. He was a leader in his profession, contributing to many important domains of science and knowledge. Franz Reuleaux was born in Eschweiler in Germany (at the time part of Prussia). His father and grandfather were both machine builders. His technical training was at the Karlsruhe Polytechnic School. He then studied at universities in Berlin and Bonn Education. After some time spent in the family business he became a professor at the Swiss Federal Institute in Zurich. Eventually, in 1879 he became Rector at the Königs Technischen Hochschule Berlin – Charlottenburg. This was a major technical institute, with about 300 professors. He became widely known as an engineer-scientist — a professor and industrial consultant, education reformer and leader of the technical elite of Germany. Reuleaux was the appointed chairman of the German panel of judges for the Sixth World Industrial Fair opened in Philadelphia on May 10, 1876. He admitted that German-made goods were far inferior to those of other countries and that German industry's guiding principle was “billig und schlecht” (English: cheap and shoddy). This shook business and evoked wide comment in the press.

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Reuleaux served on several international juries and commissions and considerably involved in formation of a patent system, as he was active in German politics.He was a member of the Royal Swedish Academy of Sciences from 1882. Contribution Reuleaux believed that machines could be abstracted into chains of elementary links called kinematic pairs. Constraints on the machine are described by constraints on each kinematic pair, and the sequence of movements of pairs produces a kinematic chain. He developed a compact symbolic notation to describe the topology of a very wide variety of mechanisms, and showed how it could be used to classify them and even lead to the invention of new useful mechanisms. At the expense of the German government, he directed the design and manufacture of over 300 beautiful models of simple mechanisms, such as the four-bar linkage and the crank. These were sold to universities for pedagogical purposes. Today, the most complete set are at Cornell University College of Engineering.[1] DEATH : He died on April 20 1905

KINEMATICS BASICS : MOTION FO BODY INDER GRAVITY ACCELERATION DUE TO GRAVITY ‘g’ Anybody in motion under the influence of gravity forms three equations as follows With respect to velocity : v= u +- gt ………………..(1) With repect to displacement h= ut +- 1/2gt2 ……………..(2) With respect to average velocity v2-u2=+-2gh………………(3) EQUATION OF MOTION FOR A FREELY FALLING BODY For a freely falling body , with initial velocity u =0 the velocity continuously increaesas it falls down through height the direction og g is toward the earth so g is taken positively Hencethe equation of the motion can be written as follows

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 From equn (1) v= u +- gt if we take u=0 and g=+g Then the equation wil be as follows v=gt From equn (2) h= ut +- 1/2gt2 if we take u=0 and g=+g Then the equation will be as h=1/2gt2 From equn (3) v2-u2=+-2gh if we take u=0 and g=+g Then the equation will be as V2=2gh

EQUATION OF MOTION FOR A BODY THROWN UPWARD When a body is thrown upwards there will be a initial velocity and it will reacha certain height and finally its velocity will become zero . the acceleration due to gravity will be –g . as it is directed away from the earth . Then the initial equation will be as follows Equation (1) wil be as : v= u -- gt Equation (2) wil be as h= ut -- 1/2gt2 Equation (3) wil be as v2-u2=--2gh

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IMPORTANT POINTS  In the case of bodies falling, the equations of motion are applied changing a to g and s to h.  a = g when the body falls down and a = — g when the body goes up.  u = 0 for a body falling freely. 

-is the maximum height reached- by a body when thrown with an initial velocity u.



is the time taken by the body to reach the maximum height and is known as time of ascent.



is the time taken by the body to reach the ground from the maximum height. This is called time of descent.  Time of flight is the time interval during which the body is in air.  Time of flight = Time of ascent + Time of descent

 When a body is projected upwards, the velocity with which it travels at any point on its path is equal to the velocity with which it moves downwards at that point.

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QUESTION FROM PREVIOU PUBLIC EXAMINATION 1. Find the velocity of a freely falling body from a height of 20m when it touches the ground. (June 2005) 2. A body is projected vertically upwards with an initial velocity of 10 m/s. Find the maximum height reached by the body . (June 2002) 3. A body is projected vertically upwards with an initial velocity of 40 m/s. Find the maximum height reached by the body.

(March 2002)

4. A body is projected vertically upwards with a velocity of 20 m/s. Find the maximum height reached by the body.

(March 2001, June 2001)

5. What do you mean by Time of flight? (March ‘12, Oct. 1999) 6. A ball is thrown up and attains a height of 80m. Find its initial speed. (March 2009,June 2006, 2004)

Short Answer Questions 1. Write the equations of motion for a freely falling body. (T.Q.) A. The equations of motion for a freely falling body are:

where v is the final velocity, g is acceleration due to gravity, h is the distance travelled in time t. 2. Write equations of motion for a body thrown upwards. (T.Q.) A. Let a body be thrown upwards with an initial velocity u. Let v be its final velocity after travelling through a height ‘h’ in time ‘t’. If g is the acceleration due to gravity then

3. Obtain a formula to find the maximum height reached by a body when it is projected vertically upwards with a velocity u. (T.Q.)

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A. 1) Let u be the initial velocity of projection of the body and h be the maximum height reached by it. 2) When the body reaches the maximum height its final velocity v = 0 3) As the body is moving upwards acceleration a = — g 4) We know 5) Substituting the values,

The maximum height reached by the body is directly proportional to the square of the initial velocity. 4. Define the terms (a) time of ascent (b) time of descent (c) time of flight. (T.Q.) (June ‘01, March ‘12) A. (a) time of ascent: The time taken by the body thrown up to reach its maximum height is called time of ascent. time of ascent ta u/g (b) time of descent : The time taken by the freely falling body to touch the ground is called time of descent. (c) time of flight: The time for which the body remains in air is called time of flight. It is equal to the sum of time of ascent and time of descent.

Very Short Answer Questions 1. For a freely falling body ‘g’ is taken as positive. Why? A. In case of freely falling body, the direction of motion of body and the direction of acceleration due to gravity (g) are same. Hence ‘g is taken as positive. 2. For a body thrown up ‘g’ is taken as negative. Why? A. In case of a body thrown up, the direction of motion of body and the direction of acceleration due to gravity (g) are opposite. Hence ‘g’ is taken as negative.

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3. What is the final velocity of a body thrown up? (or) What is the initial velocity of a freely falling body? A. Zero. 4. Define acceleration due to gravity. A. Acceleration due to gravity (g): The acceleration produced in a freely moving body under gravitational force is called acceleration due to gravity. 5. Can a body have acceleration in one direction and velocity in the opposite direction? A. Yes. In case of vertically projected body, acceleration and velocity are in the opposite directions. 6. Why should force be applied to project a body upwards? A. Every body is attracted by earth with gravitational force vertically downwards. To overcome this gravitational force, a force is required to project it up. 7. A body dropped from the top of a tower or slipped out of a moving aeroplane is called a freely falling body. Why? A. When a body is dropped from the tower or slipped out of the plane, no initial force is applied. The body falls with uniform acceleration due to action of gravity force. Hence such bodies are said to be freely falling bodies.

Long Answer Questions 1. Show that the time of ascent is equal to the time of descent. (T.Q.) A. a) Time of ascent (t1) 1) The time taken by the body thrown up to reach its maximum height ‘h’ is called its time of ascent. 2) Let ‘t1’ be the time of ascent. At the maximum height, its velocity v = 0 3) We know v=u—gt

Hence, time of ascent (t1) is directly proportional to the initial velocity u. b) Time of descent (t2) 1) The time taken by a freely falling body to touch the ground is called the time of descent. 2) The initial velocity for the downward journey is obviously zero. Let t2 be the time of descent.

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4) We know Maximum height reached

The time of ascent is equal to the time of descent in the case of bodies moving under gravity. 2. Derive a formula for the velocity on reaching the ground when a body is dropped from a height â&#x20AC;&#x2DC;hâ&#x20AC;&#x2122;. (T.Q.) A. 1) As the body is dropped its initial velocity u = 0. 2) Height from which the body is dropped s = h 3) As the body is falling, acceleration a = + g. Final velocity of the body on reaching the ground 4) Formula: Substituting the values: Velocity v = 3. Show that the upward velocity at any point in its flight is the same as its downward velocity at that point. A. a) Downward velocity at the point: 1) When a body is dropped from a height h, its initial velocity is zero. 2) Let the final velocity on reaching the ground be v. 3) For a freely falling body, we know , but u 0, therefore, b) Upward velocity at the point: -

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1) Let a body be projected vertically upwards with an initial velocity u. Since, it is moving upwards, its acceleration is ‘— g’. 2) As the body goes up, its velocity decreases and finally becomes zero (v = 0) at some point (h). This point (h) is the maximum height reached by the body. 3) We know Substituting the values: It is clear from the equations (1) & (2) that the upward velocity at any point in its flight is the same as its downward velocity at that point.

PROBLEMS 1. A stone is thrown vertically up with an initial of 10 m/s. Find the maximum height reached and the time of ascent. [Take g = 10 m/s 2] (T.Q.) (June 2002)

Solution: 1) Given: Initial velocity Acceleration due to gravity Final velocity 2) Maximum height

u =10 m/s, g = 10 m/s2, v = 0 (at maximum height) h = ?, Time of ascent ta = ?

3) Formula: 4) 2. A ball is thrown up and attains a maximum height of 80 m. Find its initial speed. [g = 10 mIs2] (T.Q.) (March 2009, June 2006, 2004) Solution: 1) Given: Acceleration a = g = 10 m/s2, Maximum height h = 80 m 2) Final velocity v = 0, Initial velocity u =? 3) Formula

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3. A stone is dropped from the top of a building and is found to reach the ground in 1 second. Find the height of the building. (T.Q.) Solution: . 1) Initial velocity Time of ascent 2) Acceleration due to gravity h =?

u = 0, ta = I second a = g = 10 m/sec2, Height of the building

3) Formula:

4) 4. Find the velocity of a stone on reaching the ground when it is dropped from a height of 19.6 m. (T.Q.) Solution: 1) Given: Height h= 19.6 m, Acceleration due to gravity (g) = 9.8 m/s2 Initial velocity u = 0, Velocity of the stone v =? 2) Formula: v2â&#x20AC;&#x201D;u2=2gs 3) v2 -02 = 2gh (or) v2 =2gh 4) v2=2x9.8x19.6=19.6x19.6 5) final velocity 5. A body is projected vertically upwards with a velocity of 20 m/s. Find the maximum height reached by the body. [Take g = 10 mIs 2] (T.Q.) (March 2001 )

Solution: 1) Given: Initial velocity u = 20 m/s, Acceleration due to gravity g = 10 m/s2, h =?2) Formula:

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Chapter-4 DYNAMICS & SIMPLE HARMONIC Motion

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INTRODUCTION Dynamics is a branch of Physics that deals with study of forces, and effect on their motion, to opposed to kinematics .which studies the motion of the object. So force is the main part of dynamics in physics. Generally dynamics deals with study of how a physical system alters itself. The fundamental physical law. Which is given dynamics was established by Sir ISSAC NEWTON . Dynamics is totally related to laws of motion invented by Newton. So it becomes a prior to understand all the laws of dynamics. The study of dynamics is under categories Linear and the rotation LINEAR DYNAMICS Linear Dynamics deals with objects moving in the line and quantities such as force, mass, inertia, displacement. Velocity, acceleration, momentum. ROTATIONAL DYANMICS Rotational dynamics is deals with the rotation of object in a curved path, as torque, movement of inertia, rotational inertia, angular displacement, angular velocity. Here in this chapter, we are going to discuss about inertia and key of on the rotational dynamics.

HISTORY Dynamic is the study of motion of various objects in the world around us. Dynamics in physics all starts with the invention of three laws of motion of body by Sir Isaac Newton. they describe the relationship between the body and the forces acting upon it and the motion that response to the forces these three law of motion was first introduced by sir Isaac Newton in mathematical principles of natural philosophy , first published in 1687.he used them to investigate many of the physical objects and systems Before the invention of laws of gravitational motion, laws invented by Kepler on planetary model took similar description of Newton. Johannes Kepler published his first two laws in 1609 Kepler discovered the third law in 1619. Kepler laws and his analysis were based on geocentric models of Aristotle and Ptolemy

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After few decades later Sir Isaac Newton proved that the relationship of keeperâ&#x20AC;&#x2122;s theory would apply under certain conditions that are fulfilled in solar system model. These are the laws of Keplerâ&#x20AC;&#x2122;s states as: 1st law of Kepler: The orbit of every planet is an ellipse with sun at one of the two foci 2nd law of Kepler: a line joining a planet and the sun sweeps out equal area during equal interval of time 3rd law of Kepler: the square of the orbit period if a planet is directly proportional to cube of the semi major axis of its orbit. FATHER OF DYNAMICS: Name: Occupation: Birth date: Death date: Education: Place of birth: Place of death:

Sir Isaac Newton Philosopher, mathematician, astronomer, physicist January 04, 1643 March 31, 1727 The king's school, university of Cambridge, trinity college Woolsthorpe, Lincolnshire, England, United Kingdom London, England, United Kingdom

BEST KNOWN FOR English physicist and mathematician Sir Isaac Newton, most famous for his law of gravitation, was instrumental in the scientific revolution of the 17th century. QUOTES "I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then in finding a smoother pebble or prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me."

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Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "acceleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree.

SCOPE OF DYNAMICS There are three main force explained in this chapter they are  CENTRIPETAL FORCE  CENTRIFUGAL FORCE  SIMPLE HARMONIC MOTION USES OF CENTRIPETAL FORCE IN OUR DAILY LIFE:  A sideway force acting on a object causing it to move in a circular path which pushes the body toward the centre is centripetal force  Whirling and object on the end of the string  Planets orbiting the sun the centripetal force is the gravity  Electrons revolving around the nucleus .the centripetal force is the attraction of negative particles toward the positively charged particles  An airplane turning in land circle the horizontal component of light provides the centripetal force  The ball bearing demonstration done in chains , the centripetal force is the normal force of the ring pushing on the ball USE OF CENTRIFUGAL FORCE IN OUR DAILY LIFE:  A force acts in a circular motion which pushes the body away from the center is called the centrifugal force

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 A centrifugal force regulates the speed of engine using spinning masse that move radially , adjusting the speed of the engine  Centrifugal force can be used to generate artificial gravity , mostly in the designing of rotating space station  Centrifugal force is also used to separate the liquid from the solid called as spin casting  It is also used in washing machine to dry and so in the clothes

BASIC CONCPETS In this lesson we are going to discuss the various types of force there are three types of forces as described below. It has a clear picture of rotational dynamics than the linear dynamics CENTRIPETAL FORCE: A particle executing uniform motion in circular path undergoes a continuous change in the direction of its velocity which results in acceleration directed towards the centre of the circular path The equation given for centripetal force works on the principle of Newton’s second law of motion We all know that Newton’s second law of motion F= m x a F = mv2 = m omega r CENTRIFUGAL FORCE: a partially executing uniform motion in a circular path undergoes a continuous change in the velocity and acceleration is directed away from the circular path The equation given for centrifugal force works on the principle of Newton’s second law of motion We all know that Newton’s second law of motion F= m x a F = mv2 =m omega r “Any motion that repeats itself along the same path in equal interval of time is called a periodic motion “

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“If particle in a periodic motion moves back and forth over the same path, its motion is said to be oscillatory or vibratory motion “ SIMPLE HARMONIC MOTION: The to and fro motion of a particle about a position on a fixed path such that directly acceleration of the particle is always directed the mean position and is directly proportional to the displacement of the particle from us mean position is called a simple harmonic motion A simple pendulum also posses the same simple harmonic motion when it swings from its fixed point, actually it is the gravitational force which makes it oscillates.

IMPORTANT POINTS  A body can have three types of motions, translatory, oscillatory or vibratory and rotatory motions.  An external force always directed towards a centre is necessary to change a translatory’ motion into a rotatory motion.  Circular motion is a special case of rotatory motion.  Angular displacement is the angle described by the radius vector of a particle in undergoing circular motion.  Radian is the angle subtended by an arc of unit length on a circle of unit radius.   The rate of angular displacement is angular velocity.  In uniform circular motion, angular velocity is constant.  The magnitude of linear velocity of the particle in circular motion is constant but its direction changes continuously.   In circular motion, the centripetal acceleration is always directed towards the centre.  Centripetal acceleration  Centripetal force  Inertial frame of reference is an imaginary coordinate system which is at rest or in uniform motion.  Newton’s laws are valid in this inertial frame of reference.  Newton’s laws are not valid in non inertial frame of reference.  Centrifugal force is a radially outward force acting on a body in a uniform circular motion in an accelerated or rotating frame.

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 Centrifugal force is equal in magnitude to centripetal force.  Centrifugal force is not a reaction force.  Centrifuge is a machine which separates particles of different densities in a given mixture.  When a vehicle is negotiating a curved road, the outer edge of the road is slightly raised above the level of the inner edge to provide centripetal force to the vehicle:  The banking angle  where v is the expected speed of the vehicle and r is the radius of curvature of the path.  A satellite is a body revolving round another body of large mass.  A body revolves round the earth when enough horizontal speed is imparted to the body.  With this principle Artificial Satellites are launched.  Any motion that repeats itself along the same path in equal intervals of time is called a periodic motion.  If a particle in periodic motion moves back and forth over the same path, then its motion is called oscillatory or vibratory motion.  The to-and-fro motion of a particle about a mean position on a fixed path such that the acceleration of the particle is always directed towards the mean position and is directly proportional to the displacement of the particle from its mean position is called a simple harmonic motion.  The periodic motion of a particle is said to be a SHM, if  The motion of a particle is vibratory about a mean position.  The acceleration of the particle is always directed towards the mean position.  The magnitude of the acceleration (a) is directly proportional to the displacement (x) of the particle from its equilibrium position, that is a

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PREVIOUS EXAMINATION QUESTIONS 1. Distinguish between a rotatory motion and a circular motion. (March 2010, 2006) 2. What is Centrifuge? How does it work? (June 2006, March 2009, 2004, April ‘08) 3. Explain the working of a laundry drier. (June ‘07, March ‘12, ‘07, ‘05, ‘03) 4. Distinguish between Centripetal and Centrifugal Force. (Mar 08, Jun 03, 2002) (June 2001) 5. Derive the formula of the banking angle, 6. What is the principle of launching a satellite into an orbit? (Jun04,00,Mar2010) 7. What is the angular velocity of the earth about its own axis? (Oct. 1999) 8. What is a centrifuge? How does it work? Give one domestic example where the principle of centrifuge is involved? (March 1999) 9. What is the necessity for banking of roads? (Oct. 1999) (June 2004)

Simple Harmonic Motion 1. Give examples for oscillatory motion observed in your day-to-day life. (June 2000) 2. What is simple harmonic motion? What are its characteristics? (June 2008) 3. Describe an experiment to determine acceleration due to gravity by simple pendulum. (March 2000) 4. Find the length of a simple pendulum whose time period is 1.2 seconds. Given g= (March 1999) 5. Find the length of a simple pendulum whose time period is 1.8 seconds. (Given g=

(March ‘99)

Short Answer Questions 1. Define angular displacement. What are its units? (T.Q.) A. The angle through which the radius vector rotates in a given time is called angular displacement. Its units are radians. 2. Define angular velocity. What are its units? (T.Q.) (March 2011)

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A. The rate of angular displacement is called angular velocity. Its units are radian I second.

3. Distinguish between a rotatory motion and a circular motion. (T.Q.) (March 2010, 2006)

4. When do you say that a body is in uniform circular motion? (T.Q.) A. If the time period (1) remains constant for any revolution of the body then the body is said to be in uniform circular motion. In a uniform circular motion, the angular velocity is constant. 5. Distinguish between inertial and non-inertial frames of reference. (March 2011) (T.Q.)

6. What is a centrifuge? How does it work? (June ‘12, ‘06, March ‘09, ‘04, 1999, April ‘08) A. A centrifuge is a machine used to separate particles of higher mass from those of lower mass in a given mixture. A centrifuge consists of a cylindrical vessel rotated about its own axis at high speed with the help of an electric motor. Eg: When milk is poured into the cylindrical vessel of the centrifuge and rotated with high speed, the particles of higher mass (skimmed milk) are thrown away

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from the centre due to greater centrifugal force and lower-mass cream particles collect at the centre, that is, near the axle.

7. Explain the working of a laundry drier. (T.Q.) (Jun‘07, Mar ‘12, ‘07, ‘05, ‘03) A. 1) Wet clothes are dropped into a cylindrical vessel containing holes. 2) When the vessel is rotated, the wet clothes get stuck to the walls of the vessel. 3) The centrifugal force pushes the water molecules from the clothes out through the holes. 4) Thus the clothes are dried. This is how laundry drier works. 8. What is the necessity of banking roads? (T.Q.) (June 2004) A. ) If there is no banking the car has to take the help of frictional force between its tyres and the road. 2) Since the frictional force is limited and is not always dependable, banking of curved roads or tracks is necessary. 3) Otherwise the car would skid. 9. What is the principle of launching a satellite into an orbit? (T.Q.) (Mar ‘01, June ‘04, ‘00)

A. The principle of launching an artificial satellite into a proper space orbit is to impart sufficient initial horizontal speed such that it revolves round the earth at the chosen height. 10. What is a periodic motion? Give an example. A. Any motion that repeats itself along the same path in equal intervals of time is called periodic motion. Eg: The motion of a pendu1umof a wall clock. 11. When does a periodic motion become an oscillatory motion? A. If a particle in a periodic motion moves back and forth over the same path, its motion is said to be oscillatory or vibratory motion. 12. How is the centripetal force provided for electrons going round the nucleus in an atom? A. In the case of an electron going round the nucleus in an atom, the centripetal force is provided by the electrostatic force of attraction between them.

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13. Give examples of centripetal force. A. 1) The gravitational force between planets and sun. 2) The force provided by the finger, for the circular motion of a stone or bob tied at one end of the string. 3) The electrostatic force between the nucleus and the electrons. 14. What are the uses of a centrifuge? A. 1) A centrifuge is used to separate sugar crystals from molasses. 2) It is also used to separate honey from bee wax. 15. Distinguish between a translatory motion and rotatory motion.

16. Distinguish between linear acceleration and centripetal acceleration.

17. When curd is churned, cream collect at the centre, while butter-milk thrown away to the sides of the vessel. Why? A. A vessel containing a mixture of two liquids of different densities is subjected to uniform circular motion. The angular velocity is same for all the particles but masses are different. The centripetal force necessary to hold the particles in circular orbit is less for lighter particles than for denser particles. Therefore, the lighter particles settle on circles of lesser radius and denser particles on circles of larger radius which means the denser liquid is separated from lighter liquid. Butter is separated from milk or buttermilk for the same reason.

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18. Explain why a cyclist bends inwards while negotiating a curve. A. If the frictional force is not sufficient the cycle skids. If he leans inwards, the horizontal component of the normal reaction of road on the bicycle provides the necessary centripetal force and hence skidding and wear and tear of tyres is avoided. The vertical component of the normal reaction balances the weight of the vehicle. 19. What is the reason for the stability of an orbiting satellite? A. The force of attraction between the earth and the orbiting satellite provides the necessary centripetal force. As the satellite is revolving round the earth in an orbit, it acquires the necessary centrifugal force. As long as the forces balance each other the stability of the satellite is achieved. 20. Why do not centripetal and centrifugal force form action and reaction pair in the sense of Newtonâ&#x20AC;&#x2122;s third law? A. Both centripetal and centrifugal force act on the same rotating body. Therefore, they do not form action - reaction pair in the sense of Newtonâ&#x20AC;&#x2122;s third law. 21. What are the uses of centrifuge? A. Uses of centrifuge: 1) Sugar crystals are separated from molasses. 2) Honey is separated from beeâ&#x20AC;&#x2122;s wax. 3) Precipitates and sediments of a non-homogeneous mixture of solution can be separated. 4) Particles of higher mass from those of lower mass are separated in a given mixture. 22. Give examples for oscillatory motion observed in your day-to-day life. A. Examples for oscillatory motion: 1) The motion of a pendulum in a wall clock. 2) The back and forth motion of the balance wheel of a wrist watch. 3) Motion of strings in musical instruments like violin, guitar etc. 4) Motion of mass attached to a spring. 5) To - and - fro motion of molecules of air as a ground wave passes by. 6) The invisible motion of atoms in a solid. 23. What are remote sensing satellites?

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A 1) Some satellites can see the areas of forests, deserts on the land and also areas on the ocean and take pictures. 2) Presence of minerals, ores and ground water in a region could be detected from the pictures sent by satellites. Such satellites are called â&#x20AC;&#x2DC;Remote sensing satellitesâ&#x20AC;?. 24. What is radius vector? A. The radius OA or OP has a direction at any point on the circle and is called radius vector represented by r. Its magnitude is just the radius r.

Simple Harmonic Motion 1. What is a periodic motion? Give an example. (T.Q.) A. Any motion that repeats itself along the same path in equal intervals of time is called periodic motion. Eg: The motion of a pendulum of a wall clock. 2. When does a periodic motion become an oscillatory motion? (T.Q.) A. If a particle in a periodic motion moves back and forth over the same path, its motion is said to be oscillatory or vibratory motion. 3. Give examples for oscillatory motion observed in your day-to-day life. (T.Q.) (June 2000) A. Examples of oscillatory motion observed in day-to-day life are 1) The motion of a pendulum of a wall clock. 2) The motion of a mass attached to a spring. 3) The invisible motion of atoms in a solid. 4) The oscillation of a swing. 5) The motion of a balance wheel of a wrist watch. 4. Are all vibratory motions SHM? Justify your Answer. (T.Q.) A. All vibratory motions need not be simple harmonic motions. A vibratory motion becomes S.H.M. only if it satisfies the following properties. 1) The motion of particle is vibratory about a mean position. 2) The acceleration of the particle is directed towards the mean position.

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3) The magnitude of acceleration is directly proportional to its mean position. i.e., a

Very Short Answer Questions 1. What is a centripetal acceleration? (T.Q.) A. A particle executing uniform circular motion undergoes a continuous change in the direction of its velocity which results in an acceleration directed towards the centre of the circle called centripetal acceleration. 2. What is a centripetal force? (T.Q.) A. The force which continuously deflects a particle from its straight line path and makes it to travel along a circular path is called centripetal force. It is always directed along the radius towards the centre of the circle. 3. What is the direction in which sparks fly when a knife is pressed on a rotating grind stone to sharpen the knife? (T.Q.) A. Tangential to the grind stone. 4. Why is a centrifugal force called a fictitious force? (T.Q.) A. Centrifugal force is a pseudo force in an inertial frame of reference because it cannot be associated with any agent or object. Hence it is also known as a fictitious force. 5. What is banking angle? (T.Q.) A. The angle made by the line joining the outer raised edge of the road to the inner edge with horizontal line is called the banking angle. 6. What is a translatory motion? A. The motion Of a body along a straight line path is called translatory motion or linear motion. 7. What is meant by oscillatory motion? A. If a particle in a periodic motion moves back and forth over the same path, its motion is said to be oscillatory or vibratory motion. 8. What is meant by a rotatory motion? A. A body is said to be in rotatory motion if every particle moves in a curved path about a fixed point. 9.â&#x20AC;&#x2122; Define time period of a particle. A. The time period (Iâ&#x20AC;&#x2122;) of a particle in a circular motion is defined as the time taken by it to complete one revolution. 10. Define centrifugal force.

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A. The radially outward force on a body in a uniform circular motion, observable only in a rotating frame of reference is called centrifugal force. 11. Define ‘Dynamics’. A. The study of motion of a body under the action of a force is called ‘Dynamics’. 12. Define radian. A. The angle subtended by an arc of unit length on a circle of unit radius is called radian. 13. What is radius vector? A. The line joining the particle (under uniform circular motion) to the centre of the circle is called a radius vector. 14. State the reason for the bulge of the earth of the equator. A. During the formation of the earth the particles near the equator experience more centrifugal force.

Simple Harmonic Motion 1. Give two examples of simple harmonic motion. A. The two examples of simple harmonic motion are: (i) Spring mass system, (ii) Water levels in U-shaped tube. 2. What is meant by seconds pendulum? A. The simple pendulum whose time period is 2 seconds is called seconds pendulum. 3. What is the relation between l, T and g? A. The relation between l, T and g is 4. What is the relation between time period and length of the pendulum? A. Time period is directly proportional to the square root of the length of the pendulum 5. What happens to the oscillations of simple pendulum when His taken to the centre of the Earth? A. Since the value of ‘g’ is zero at the centre of the Earth the simple pendulum does not oscillate. 6. What is the value of acceleration due to gravity at a place found by using simple pendulum. A. Acceleration, due to gravity g = 9.8 m/s2.

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Long Answer Questions 1. Distinguish between centripetal and centrifugal force. (T.Q.) (March ‘08, ‘02, June ‘03, ‘02)

2. What is angle of banking ? Deduce an expression to find its value. (Or) Derive the formula, the banking angle : A. Angle of banking : ‘The angle made by the line joining the outer raised edge of the road to the inner edge with the horizontal line is called banking angle’. DERVIATION: 1) Let ‘1’ be the width of the path AB and ‘0’ be the angle of banking. 2) AC represents the horizontal path. 3) Let a body of mass ‘m’ moving with a velocity ‘v’ be negotiating a curved path of radius ‘r’.

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4) The normal reaction ‘R’ acts normal to the path AB. 5) This reaction ‘R’ can be resolved into vertical and horizontal components and as shown in the diagram. 6) The vertical component

7) The horizontal component

is balanced by the weight ‘mg’ of the body:

provides the centripetal force.

8) From equations (1) and (2)

3. Derive the relation . A. 1) Consider the particle P moving with uniform speed v. 2) Let the time taken by the particle to go from position P (t1) to position P (t2) be & and the angle swept by the radius vector r be . 3) Then, AP becomes an arc Length of the arc 4) Time taken by P to travel this linear distance =

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4. What are the uses of artificial satellites? A. Uses of artificial satellites: 1) Artificial satellites help to develop reliable communication links over the entire globe. 2) Telephones, Fax, INTERNET are examples for such global level communications. 3) These are used to the ‘weather prediction’. 4) The artificial satellites are used for remote-sensing. With the help of the pictures sent by these satellites proper steps are taken to prevent deforestation and expansion of deserts. 5) Satellites and space stations are used for the study of Astronomy. 6) Some satellites have also been used for spying in the defence service. 5. Define centripetal and centrifugal forces. Mention two examples for each. A. Centripetal force: The force which acts continuously on a particle initially moving with a linear velocity and makes it travel along a circular path is called centripetal force. Examples: l)The gravitational force between planets and sun. 2) The electrostatic force between the nucleus and the electrons. 3) The force provided by the finger, for a circular motion of a stone or bob tied at one end of the string. Centrifugal force: The radially outward force on a body in a uniform circular motion, observable only in a rotating frame of reference, is called centrifugal force. Examples: 1) Centrifuge 2) Banking of roads 3) Centrifugal pump.

Simple Harmonic Motion 1. What is simple harmonic motion? What are its characteristics? (3.Q.) (June ‘10, ‘08, ‘05) A. Simple harmonic motion: The to-and-fro motion of a particle about a mean position on a fixed path such that the acceleration of the particle is always directed

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the mean position and is directly proportional to the displacement of the particle from its mean position is called a simple harmonic motion. Characteristics of S.H.M.: 1) a constant time period (T) or a constant frequency 2) an amplitude (A) and 3)a constant mechanical energy which is the sum of potential energy and kinetic energy at every point in the path of oscillation. 2. Describe an experiment to determine acceleration due to gravity by simple pendulum. (T.Q.) (March 2000) A. Determination of’g’ by simple pendulum: 1) First the length ‘1’ of the simple pendulum is noted. A pointer is placed in front of the bob. When it is in its mean position at ‘0’. 2) The bob is slightly pulled aside and released. The bob begins to execute S.H.M. 3) When the bob is crossing the mean position ‘0’ from left to right start a stop watch. 4) Again when the bob moves from left to right and crossing the mean position ‘0 count it as ope oscillation. 5) Count like that 20 oscillations and stop the stop watch when it completes the 20th oscillation. The time ‘t’ taken for 20 oscillations is noted. 6) The same experiment is repeated for second and third trials. The average value (ta) of the three trials of time is found out. The time period determined. . 7) The length of the simple pendulum is changed to 40 cms, 50 cms, 60 cms and 70 cms and in each case the time period is calculated. The observations are tabulated. Simple harmonic motion of a simple pendulum

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Average value of

8) Now acceleration due to gravity

is determined.

Diagrams 1. Sketch a neat diagram of simple pendulum executing simple harmonic motion. A.

2. Sketch a neat diagram of a spring balance attached with a mass executing simple harmonic motion.

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3. Show the diagram of oscillation of water level in a U - tube executing S.H.M.

A. 4. Draw the neat diagram of banking of roads and label the parts.

PROBLEMS 1. An object is moving along a circle of radius 6 m with a constant speed of 12 m/s. Calculate its angular velocity.(T.Q.) Solution:. 1) Given Radius (r) = 6 m, Velocity v = 12 m/s 2) Formula:

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3) .. Angular velocity 2 The speed of a wheel is 1800 r.p.m. Find its average angular velocity in rad/s. (T.E.) Solution: 1) Given: No. of revolutions per minute (60 see) = 1800 frequency (f) of revolution

= 30 rev/sec.

2) Formula: Angular velocity 3) :. Angular velocity

188.57 rad/sec.

3. What is the angular velocity of the earth about its own axis? (Hint: I day = 24 hours)(T.Q.) (Oct. ‘99) Solution: 1) Given: Time for 1 revolution T = 24 x 60 x 60 sec. revolutions / sec.

2) .. Frequency of revolution of earth 3) Formula: Angular velocity

4. A curved road of l00m radius is banked with an angle of 10°. Find the safe velocity for a vehicle moving on the road. (T.E.) Solution: 1) Given: Radius (r) 100 m, Angle of banking Safe velocity v =? , We know g 9.8 m/s2

= 10°

2) Formula:

4) From Tables of Natural tangents

= 0.1763

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5. A particle undergoes an angular displacement of 90째. What is the value of the angular displacement in radians and revolutions? (T.Q.) Solution: . 1) Given: Angular displacement = 90째. 2) We know 360째 radians. 4) We know 360째 = 1 revolution.

6. A stone moving along a circular path makes 20 revolutions in 10 seconds. What is the angular velocity of the stone? (T.Q.) Solution: 1) Given: No. of revolutions made in l0s = 20 2) No. of revolutions made in 1 sec. = frequency 3) Formula: Angular velocity, 7. Find the acceleration of the moon towards the earth. Given: Time taken by the moon to complete one revolution about the earth T = 27.3 days. Distance between the earth and the moon r = 3.85 X 10 km 3.85 x 108 m. (T.E.) Solution: 1) Given: T = 27.3 days 27.3 x 24 x 60x 60 sec. distance, r= 3.85 x108 m 2) Formula: Centripetal acceleration, a= 3) But 8. The radius of curvature of a road is 60 m. It is to be banked so that no friction - force is required for a car travelling on the road at 25 m/s. Find the angle of banking. (T.Q.) Solution:

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1) Given : Radius r 60 m, Velocity v = 25 m/s Angle of banking =?, Acceleration due to gravity, g 9.8 m/s2

Without the friction, the car would slip inwards if its speed is less than.25 m/s and outwards if its speed is greater. 9. A satellite revolves with a time period of 84.3 minutes at a height of 40 km. from the surf ace of the earth. Find the speed of the satellite. The radius of the earth is 6400 km. (T.E.) Solution: 1) Given: Radius of the orbit of the satellite r = radius of the earth + height of the satellite from the surface of the earth 6400 + 40 = 6440 km. 2) .. r = 6440 km = 6440000 m 3) Time period T = 84.3 minutes = 84.3 x 60 sec. = 5058 sec.

5) Formula: Speed of the satellite v = . 6) .. v = 64,40,000-x 0.0012 =8,000 m/s.

Simple Harmonic Motion 1. Find the length of a simple pendulum whose time period is 1.2 seconds. Given g = 9.8 in/sec2. (T.Q.) (March 1999) Solution: I) Given: Time period T = 1.2 seconds Acceleration due to gravity, g = 9.8 rn/sec2 Length of the simple pendulum 1 =7 2) Formula:

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2. In a simple pendulum experiment the value of Find the value of ‘g’ at that place. (T.Q) Solution:

found to be 0.248 rn/s2.

I) Given: Value of = 0.248 m/sec2 Acceleration due to gravity g =?

3. Find the time period of a simple pendulum whose length is 100 cm. (Given g = 9.8 rn/sec2.) (T.E.) Solution: 1) Given: length 1 = 100 cms, and g = 9.8 mIs2 Time period T =7 2) Formula: 3) (or)T= 4) ..T=2x3.14x =2sec. This pendulum is called a seconds pendulum because its time period is 2 seconds. 4. Time period of a simple pendulum on the moon is 5 seconds. If its length is 105 cm, find the acceleration due to gravity on the moon. (T.E.) Solution: 1) Given: Time period T = 5 seconds, length I = 105cm = 1.05 m 2) Formula: 3) 5. Find the length of a simple pendulum whose time period is 1.8 seconds. (Given g= 9.8 m/s2). (March’99) Solution: 1) Given T = 18s, g= 9.8 mIs2, l=? 2) Formula: g=

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Chapter-5 ELECTROMAGNETIC SPECTRUM

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INTRODUCTION: The word electromagnetic spectrum is offently used in many of the fields of science such as in biology for the use of photosynthesis. We need electromagnetic spectrum in the area of astronomy. Electromagnetic radiation is often a part of discussion of radioactive materials, even the sun rays contain many electromagnetic spectrum, even in the field of chemistry we would have come across the word spectrum. There it is referred as differ in electron analysis and characteristic properties of element. In physics it is a study of waves, electrons, and magnetism. The electromagnetic spectrum is the range of waves produced when charged particles are accelerated or change their energy state. The light you see is a form of electromagnetic force, typically produced, when electrons lose energy the lost energy is emitted in the form of electromagnetic spectrum. Most parts of electromagnetic spectrum are used in science for spectroscope and other probes interaction as ways to study and character type matters. In addition, radiation from various parts of spectrum has found many others used for communication and manufacturing.

HISTORY: For most of the years light was the only known part of electromagentic spectrum which we call as visible light. The ancient Greek studied that light travels in a straight line. Till 16th century it was confusion in the understanding that light is a wave or a particle. Some recognized as a wav and some recognized it a particle The first discovery of electromagnetic spectrum other than the light came in year 1800. When William Herschel discovered that IR radiations. He discovered it when he was experimenting with light by moving a thermometer with the help of prism, he found that the highest temperature was beyond the red. Thus changes were due to invisible IR rays. Then it was Johann Ritter who worked at the other end and found chemical rays Electromagnetic radiation was first linked to electromagnetism in 1848, when Michael faraday noticed that light travels through a transparent material responded to electric field

www.gnanmantra.com Maxwell equation predicted an infinite number of frequencies of electromagnets were all travelling at the same speed of light. this lead to existence of entire Electromagnetic radiation In 1886 the physicist Heinrich hertz built an apparatus to generate and detect what we now called as radiances. Hertz demonstrated that the new radiation could be both reflected and refracted by various dielectric media, in the same manner as light. In 1895 Wilhelm Rontgen noticed a new type of radiation emitted under evacuated tube subjected to a high voltage called X- rays which used in medical field In the last rays of electromagnetic spectrum was gamma rays include by Paul Villard in 1900 when he was studying radioactive emission of radium Edward Andrade found that gamma rays were similar to alpha ray but with shorter than the wavelength and higher frequency . DECRPTION ON ELECTROMAGNETIC SPECTRUM As we all know when a visible light is allowed to pass through a prism there are different types of rays the outcome such as. X- Rays, UV -Rays. Gamma rays, Micro waves, etc. so we will see the description of each of the rays as follow. VISIBLE SPECTRUM: the visible region of the electromagnetic spectrum is the common one, as it is seen to everyoneâ&#x20AC;&#x2122;s eye. The range of visible spectrum extends from 0.4 to0.7 that is in the form of violet color to red color. Visible spectrum is evolved when the valency electrons mps back to the normal state. IR SPECTRUM: infrared radiations have wavelength larger than those of the visible light that is from the 0.7 to 100. They are emitted when the molecules change the state of its motion either to rotational or vibrational. Heat from hot both bodiesâ&#x20AC;&#x2122; travels in the form of IR radiation and therefore all hot bodies form sources of IR radiation.

www.gnanmantra.com MICROWAVES: these range from wavelength from 10 to 10 these waves are commonly produced by electromagnetic oscillators with high frequency from 109 1011 in an electric circuit. They are also used to transmit telephone conversation. RADIO WAVES: Radio waves have wavelength from 10 to 100km they are produced by the electromagnetic oscillators of low frequency. These radiations are created when electrons are accelerated in as suitable electronic circuit ULTRAVOILET SPECTRUM : the radiations of wavelength shorter than the visible light rays ranges from about 0.4 to 1 are called ultra violet rays these radiations are produce by the transition of electrons in the atom long term exposure of UV rays can burn your skin . The main source of UV Rays is the sun, it com along with the sun X-RAYS: These are the longer wavelength ranges from 10 to 100 can easily penetrate through soft tissues of human body but cannot pass through the bones. Of this reason these are called as soft X-rays are used in the medical diagnosis called radiography. The method to use and cure the disease is called radiotherapy GAMMA RAYS : These are the electromagnetic radiation with shortest wavelength ranging from 0.0001nm to 0.1 natural radioactive material like uranium 235 emit these type of radiations these are emitted when nucleus come to its ground state . Exposure to intense gamma radiation leads to harmful effects on human body.

IMPORTANT POINTS  A spectrum is a group of wavelengths or frequencies.  Electromagnetic radiations are transverse in nature.  When excited valence electrons in atoms jump to the if normal states, visible spectrum is emitted.  In electromagnetic radiations, electric and magnetic fields oscillate perpendicular to each other and perpendicular to the direction of propagation.  When molecules change their states of rotational or vibrational motion, infrared radiations are emitted.

www.gnanmantra.com  In electric circuits high frequency electromagnetic oscillators produce Microwaves.  In electronic circuits accelerated electrons produce Radiowaves.  By the high energy transitions of electrons in atoms ultraviolet radiations are produced.  X-rays are produced in discrete wavelengths in individual transitions among the inner electrons of an atom.  X-rays in continuous wavelengths can be produced when electrons are decelerated.  In Radioactivity Gamma rays are emitted.

PREVIOUS EXAMINATION QUESTIONS 1. Draw and label the diagram showing various regions of electromagnetic spectrum and their wavelength ranges. (June 2007, March 2006) 2. What is Radiography? (March 2003) 3. What are the uses of hard X - rays? (June 2001) 4. Draw the diagram of electromagnetic wave. (June 2005, March 2001) 5. What is the reason of depletion of Ozone layer in atmosphere? (Jun 06, Mar 00)

Short Answer Questions 1. What are the various types of electromagnetic radiations? A. Electromagnetic radiations are seven types. They are: 1. Visible 2. IR spectrum 3. Microwaves 4. Radiowaves 5. UV spectrum 6. X rays 7. — rays 2. What are the common features among all the electromagnetic radiations? A. The common features among all the electromagnetic radiations are: 1) They all can be described in terms of oscillating electric and magnetic fields perpendicular to each other and hence are called electromagnetic (e.m.) radiations. 2) These electric and magnetic fields are found to oscillate perpendicular to the direction of propagation of radiations.

www.gnanmantra.com 3) All electromagnetic wave are transverse in nature. 4) All these radiations travel with the same speed, that is the speed of light (C) in vacuum. 3. Draw the diagram of electromagnetic wave. (June 2005, March 2001) Draw a rough sketch of propagation of Electromagnetic Wave.

Parts:

Electromagnetic wave

Oscillating electric field vector

Oscillating magnetic field vector

4. Distinguish between soft and hard X-rays.

5. Distinguish Micro waves and Radio waves.

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Very Short Answer Questions 1. What is a spectrum? (T.Q.) A. A group of wavelengths or frequencies is called a spectrum. 2. What are electromagnetic radiations? (T.Q.) A. The waves traveling with velocity of light and consisting of oscillating electric and magnetic fields perpendicular to each other and also perpendicular to the direction of their propagation are called electromagnetic waves. 3. What are the uses of Hard X - rays? (June 2001) A. 1) Hard X - rays are used for testing of materials in industry. 2) They are also used to determine the structure of materials. 4. What is the reason of depletion of ozone layer in atmosphere? (June 06 , Mar 00) A. Atmospheric ozone is depleted as a result of chemical reactions with fluoro carbons. (Or) Because of fluoro carbons released from aerosol sprays, refrigeration equipment and other pollutants. 5. What is meant by Radiography? (March 2003) A. Diagnosis of a disease by the use of soft X - rays is called radiography. 6. What is the velocity of light in vacuum? A. 3x108m/sec. 7. What are used to observe the IR radiations? A. Prisms made of UP rock salt are used for observing the IR radiations. 8. Mention the devices used to detect IR radiations. A. IR radiations can be detected by devices like thermometers, thermopiles, bolometers etc. 9. What is meant by Radiotherapy? A. Cure of disease by the use of soft X - rays is called radiotherapy. 10. Write the uses of X-rays. A. (1) X - rays of short wavelengths are used to determine the structure of materials. (2) X - rays are also used for testing of materials in industry. 11. What are the uses of soft X-rays?

www.gnanmantra.com A. Soft X - rays are used in medical diagnosis. These are also used to cure some diseases. 12. Mention the uses of infrared (IR) radiations. A. 1) JR radiations are used in physio-therapy. 2) These radiations are also used to take photographs of objects in darkness. 13. What are the applications of Microwaves? A. 1) Microwaves are of ten used in RADAR, telemetry and microwave ovens. 2) Microwaves are also used to transmit telephone conversations. 3) The satellite communications also utilise microwaves. 14. What is radio astronomy? A. Mapping of the radio emissions from extra teirestrial sources is known as â&#x20AC;&#x2DC;radioastronomyâ&#x20AC;&#x2122;.

Long Answer Questions 1. In what way the various types of electromagnetic radiations differ from one another? How are they produced? (T.Q) A. Various types of electromagnetic radiations differ from one another due to the difference in their wavelengths or frequencies .

www.gnanmantra.com 2. Discuss the different types of electromagnetic radiations. Mention their wavelength ranges. (T.Q.) A. 1) Visible spectrum: The wavelength of the visible spectrum extends from about to 0.7µm, that is, from violet colour to red colour. Visible spectrum is emitted when the excited valence electrons in atom jump back to their normal states. 2) Infrared (OR) spectrum: Infrared radiations have wavelengths larger than those of visible light. That is from 0.7µm to about 100 p.m. They are emitted by molecules when, they change their states of rotational or vibrational motion. 3) Microwaves: Microwaves are electromagnetic waves with wavelengths in the Range 10µm to 10 nm. These waves are commonly produced by electromagnetic oscillators with high frequency in electric circuits. 4) Radio waves:Radiowaves have wavelengths from 1 m to about 100 km. They are produced by the electromagnetic oscillators of low frequency. 5) Ultraviolet (UV) spectrum: The radiations of wavelength shorter than the visible light ranging from about to 1 nm are called ultraviolet (UV) radiations. These radiations are produced by the transitions of the electrons in atoms. 6) X. Rays: Wavelengths of X - rays range from 0.001 nm to 10 nm. X - rays are produced when incident electrons are decelerated inside the target atoms. 7) Gamma rays: Wavelengths of gamma rays range from 0.0001 nm to 0.1 nm. emits gamma rays. Natural radioactive substances like

Diagrams 1. Draw and label the diagram showing various regions of electro-magnetic spectrum and their wavelength ranges. (June ‘07, March 2006)

www.gnanmantra.com Various regions of electromagnetic spectrum and their wavelength ranges 1. Visible spectrum 2. JR spectrum 3. Microwaves 4. Radio waves 5. UV spectrum 6. X - rays 7. -rays 2. Draw a neat diagram of prism and show the formation of visible spectrum.

Visible spectrum

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UNIT-6 SOUND

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INTRODUCTION Sound is a mechanical wave that travels through some medium like air, water, and solid etc... Composed of frequencies motion are within the range of theory. Sound is a form of vibration. These vibration create sound waves when move through the various medium. A Sound wave is a disturbance in air which results in vibration. This vibration can come from a framing fork, a guitar string, the color of air in an organ pipe. Dogs can hear sound at higher frequencies than humans, along them to hear noise that we canâ&#x20AC;&#x2122;t. The scientific study of sound is called acoustics. A sound waves are often simplified in terms of sinusoidal plane which are the main properties of sound wave are frequencies, wavelength, wavelength number, amplitude, speed, of sound direction The speed of sound depends on the waves pass through a medium. In general a sound wave is proportional to the square root of the ratio of elastic modules of the medium. In this chapter we are going to discuss how sound travels through various mediums and its daily way. Yes it is true that we have discussed about the sound in the previous classes but still here we are going to learn something new about the sound and its law

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HISTORY (LEONARDO DA VINCI ) What is Sound actually? It is wave that produced in air when we vibrate any source such as string. A simply disturbance is air caused to vibration by some source. So when was it discovered and how come let us see the fact. Leonardo Da Vinci the famous Italian thinker and artist is usually credited with the discovery of sound. This made the discovery in 1500. Leonardo was singing in a church in Riming. When he got the idea that sound waves. He was alone sitting at a window. At the house where he was born there was a small spot where he made echoes. The next was the Pythagoras in 6 th century. When someone was playing a stringed instrument, he observed that the string was being pulled, he saw the within of blurred area of the motion of the string with the perceived conductors of sound. He related it to as amplitude of vibration. Around 250BC, Aristotle also observed that the vibrating string was actually string the air , he also concluded that each bit of air struck a neighbor bit of air , which struck the other and soon , from this Aristotle hypothesis that air is a medium through which sound travels easily. In the period of 500AD the connection between the motion of sound and motion of wave was related .the roman philosopher. Anicius Maxilus Boethius specifically compared of sound through the air to the waves produced by dropping a pebble into calm water The invention of the tunings fork in 1711 by John Shore and its further development by Frenchman Rudolph Koning eased the study of sound considerably. Later breakthrough in sound were made when in 1842, Christian Doppler first identified and quantified the change in pitch that occurred when a source an observer moves towards or away from a

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stationary source of sound. This effect now been his name and is known as Doppler Effect.

USES OF SOUND: Resonance is an important phenomenon n the nature. The following are some of example of re resonance phenomenon  When soldiers cross a suspension bridge, they are asked to break their steps. this is because if frequency of the vibration of their marching becomes equal to the natural frequency of the bridge , the bridge would vibrate with a large amplitude due to resonance and the bridge could collapse  A pronounced rattling sound may occur in car when its travelling at a particular speed, but it travels faster or slower than its speed no rattle occurs. this is due to the resonance between the car engine and the body of the car  When we tune a transistor radio, we are actually adjusting its natural frequency to that of the incoming carrier electromagnetic waves from a radio transmitter. when the two frequency match maximum energy is absorbed from the incoming wave and the sound is clearly heard with appreciate amplitude  Consider a child on swing. When the swing is given series of push by the mother of the child with a frequency equal to the natural frequency of the swing the swing oscillates with larger amplitude. in this case resonance occurs between the oscillatory force applied by the mother and the swing

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BASICS ABOUT SOUND Sound is basically used in the various forms in our daily life. But there are some basic concepts that5 we need to learn so let us see. Before going to know what is the meaning of sound. We need to know that sound is a form of vibrations. So let us know what vibration is FREE VIBRATION : when a body is set into vibrations and then left itself, the vibration are called natural or free vibration DAMPED VIBRATIO N: the periodic vibration of decreasing amplitude are called damped vibration FORCED VIBRATION : when a body executes vibration under the action of an external periodic force, then the vibration is called as forced vibration RESONANACE: it is a phenomenon in which if one of the two bodies of the same natural frequency is set into vibration, the other body also vibrates with larger amplitude under the influence of the first body. Let us see a sample experiment to prove the resonance works in the daily life Arrange two hollow sound boxes that opened at one end such that their opened face each other. Mount tuning fork A and B of the same frequency on them if one of the forks is vibrated the other also vibrates automatically in the influence of first tunning fork. The air column in the first box travel while the tuning fork vibrates and makes the air column in the other box to vibrate by which the tuning fork on the box B vibrates with the influence of the first one . Note that A and B tuning fork are at same natural frequency Sound travels in the air and other source and forms two types of waves while travelling in the medium they are

PROGREESIVE WAVE and STATIONARY WAVE PROGRESSIVE WAVE: A wave that is produced in a source and travelling forward in the medium is called progressive wave. When a stone is dropped on in the water and a wave is produce in the water and disturbs the water forming a wave this type of wave is an example of progressive wave. These waves produces CREST and TROUGHS while travelling in the medium. the distance between two successive crest and trough is lambda

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STATIONARY WAVE: These waves are formed when two waves of equal frequency and equal amplitude travel in opposite direction along the same path. It produced nodes and antinodes the distance between successive nodes or antinodes is lambda /2 Further in the chapter the velocity of sound in the air is explained with a help of tuning fork experiment which we will discuss in the detail

IMPORTANT POINTS  Natural or free vibrations are the vibrations made by a body set to vibration and then left to itself.  Damped vibrations are periodic vibrations with decreasing amplitude.  Forced vibrations are those a body executes under the action of a strong external periodic. Force whose frequency is different from its, natural frequency.  Resonance is the phenomenon in which if one of the two bodies of the same natural frequency is set into vibrations, the other body also vibrates under the influence of the first body.  When a wave originating in a source continues to travel forward in a medium without returning to the source, it is called a progressive wave.  When the displacement of particles of a medium is at right angles to the direction of propagation of the wave, the wave is said to be a transverse progressive wave.  When the displacement of particles of a medium is parallel to the direction of propagation of the wave, the wave is said to be longitudinal wave.  Stationary wave (or a standing wave) is defined as the resultant wave formed when two waves of equal frequency and amplitude travel in opposite directions along the same path.  Stationary waves are characterised by nodes and antinodes.  The distance between two successive nodes or antinodes is equal to  In a stationary wave, energy remains trapped in a fixed region.

cm.

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 Velocity of sound in air is given by where ratio of specific heat of air at constant pressure (Cp) and specific heat at constant volume (Cv).  Velocity of sound is given by  Stationary waves are formed, in a resonating air,-column.

and in the

second mode  The velocity of sound in air is found from

PREVIOUS EXAMINATION QUESTIONS 1. What i a resonating air column? (March 2012, 2006) 2. Describe the experiment to find the velocity of air by Resonating Air Columns. (June 2005) 3. In a resonating air column experiment with a closed end tube, first resonance occurs when the length of the air column is 10cm. Find out the length of the air column for the occurrence of the second resonance (March 2004) 4. Distance between a node and the next antinode in a stationary wave is’ 10 cm. Find the wavelength. (April 2008, March 2003) 5. Distinguish between a progressive and stationary waves. (March ‘09, 2002) 6. Explain the phenomenon of Resonance. (Mar10, 08, 2005, 2002, June 2008, 2005) 7. Mention few incidents of Resonance phenomenon observed in your day to day life.(Mar 01, June 01) 8. Describe a method to determine the velocity of sound in air. (Jun06, 04, 00) 9. Distinguish between Node and Antinode. (March 2000) 10. Draw a figure showing the formation of a stationary wave. (October 1999) 11. What is damped vibrations? (March 2007) 12. Define node and antinode (June 2007)

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Short Answer Questions 1. Explain the terms natural and forced vibrations. What is the difference between them?(T.Q.) A. Differences between Natural vibrations and Forced vibrations:

2. Explain the phenomenon of resonance. (June 2012, 2008, March 99) (T.Q.) (Imp) A. At resonance, rapid transfer of energy takes place resulting louder sound (booming sound). If two bodies having same natural frequency are placed side by side and if one of them is made to vibrate the other will automatically begin to vibrate. This effect is called resonance. 1) Arrange two hollow sound boxes opened at one end such that their open ends face each other. 2) Mount two tuning forks A and B of the same frequency on them as shown in the figure. 3) If one of the forks A is set into vibration the other fork â&#x20AC;&#x2DC;Bâ&#x20AC;&#x2122; also begins to vibrate with larger amplitude and a loud sound is heard due to resonance.

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3. What is the difference between Nodes and Antinodes? (March 2000)

4. When soldiers march on a bridge they are asked to step out. Why? A. When soldiers cross a suspension bridge they are asked to break their steps. This is because if the frequency of vibration of their marching becomes equal to the atural frequency of the bridge. Then the bridge would vibrate with a larger amplitude due to resonance and the bridge would collapse. 5. A pronounced rattling sound may occur in a car when it is travelling at a particular speed. Why? A. A pronounced rattling sound may occur in a car when it is travelling at a particular speed, because resonance takes place between car engine and the body of the car. 6. What is the difference between resonance and forced vibrations?

7. Give two examples of resonance: A. Examples of Resonance: I) Ratting sound is produced in a car travelling with a particular speed. The sound is due to resonance between the car engine and body of the car. ii) If two simple pendulums of equal lengths are placed nearer and if one is set to oscillate, the other also begins to oscillate with a larger amplitude. This is due to resonance.

www.gnanmantra.com 8. What is the difference between damped vibrations and undamped vibrations?

9. What is end - correction in a resonating air column experiment? A. In a resonating air-column experiment an antinode is actually formed just above the glass tube but where as the length of air column is considered upto the end of the glass tube from water level. The difference in these two lengths is considered to be the end - correction ‘e’.

Very Short Answer Questions 1. What is damped vibration? (T.Q.) (March 2013, 2007) A. The periodic vibrations of decreasing amplitude are called damped vibrations. 2. What is a resonating air - column? (T.Q.) (March 2012, 2006) A. When the natural frequency of the air column coincides with the frequency of the vibrating tuning fork, the air- column would be in resonance with the tuning fork. Such an air column is called a resonating air - column. 3. Explain the phenomenon of Resonance. (T.Q.) (Mar ‘10, ‘08, ‘05, ‘02, Jun ‘10, ‘05) A. The phenomenon in which if one of the two bodies of the same natural frequency is set into vibration, the other body also vibrates under the influence of the first body. 4. Define node and antinode. (June ‘07) A. Node In a stationary wave, the point at which the particles are at rest is called a node. Antinode: In a stationary wave, the point at which the particles are having maximum displacement is called an antinode. 5. What happens when the length of the simple pendulum is decreased? A. When the length of the simple pendulum is decreased its time period (1’) decreases,

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It means

6. Define a stationary wave. (March 2011) A. The resultant wave obtained by the combination of two progressive waves of equal frequency and amplitude travelling in opposite directions along the same path is called a stationary wave. 7. What is the formula used to calculate the velocity of sound in gases?

8. A node is created on the surface of water in the glass tube. Why? A. On the surface of water in the glass tube which acts as the rigid end, the air particles are not free enough to vibrate longitudinally. Therefore a node is formed at this point. 9. An antinode is created at the open end of the glass tube why? A. At the open end of the glass tube, the air particles are free to vibrate and hence it acts always as an antinode. 10. What are free vibrations? A. When a body is set into vibration and then left to itself, the vibrations are called natural or free vibrations. 11. What is meant by natural frequency? A. the frequency of a body which produces natural vibrations is called natural frequency. 12. If we strike a tuning fork and then press its stem against the top of a table the sound becomes louder. Why? A. If we strike a tuning fork and then press its stem, against the top of a table, the sound becomes louder because the table is forced to vibrate with the frequency of the tuning fork. 13. On what factors does the frequency of a body depend? A. The frequency of a body depends on its a) elastic constants b) dimensions and c) mode of vibration.

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14. Define a progressive wave. A. When a wave continuously moves forward in a medium without being reflected at any point in the path, it is called progressive wave. 15. Do the vibrating particles of the medium move forward along with the progressive wave? Why? A. No. The vibrating particles of the medium do not move forward along with the progressiveâ&#x20AC;˘ wave but the vibrating particles of the medium transfer energy to other particles. Long Answer Questions 1. Describe an experiment to demonstrate resonance and forced vibrations. (T.Q.) A. Resonance between two or more bodies of the same natural frequency is a particular case of forced vibrations. 1) Take four identical balls A, B, C and D and suspend them from the same support from a rubber tube MN at different points as shown in the figure. A and B are pendulums of same length. So their natural frequencies are the same. 2) Pendulum D is a little longer than A and B and pendulum C is a little shorter than A and B. The two pendulums of unequal length C and D are suspended on either side of B. 3) Set the pendulum A into vibrations. Then, along with the pendulum B, the pendulums C and D also vibrate, but with smaller amplitudes. 4) However, the frequency of vibrations of B, C and D is same and is equal to the impressed frequency (due to A). 5) Pendulums C and Dare said to be in the state of forced vibrations while the pendulum B is in resonance with A. 6) The pendulums C and D make forced vibrations with smaller amplitude because their lengths are different from that of A and B.

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2. Describe a few incidents of Resonance phenomenon observed in your day to day life. (T.Q.) A. Resonance is an important phenomenon in nature. (June 2001, March 2001, 2000 1999) The following are some examples of resonance phenomenon: A. 1) When soldiers cross a suspension bridge, they are asked to break their steps. 2) This is because lithe frequency of vibration of their marching becomes equal to the natural frequency of the bridge, the bridge would vibrate with a large amplitude due to resonance and the bridge could collapse. B. 1) A pronounced rattling sound may occur in a car when it is travelling at a particular speed, but if it travels faster or slower than this speed no rattle occurs. 2) This is due to the resonance between the car engine and the body of the car; C. 1) When we tune a transistor radio, we are actually adjusting its natural frequency to that of the incoming carrier electromagnetic waves from a radio transmitter. 2) When the two frequencies match, maximum energy is absorbed from the incoming wave and the sound is clearly heard with appreciable amplitude. D. 1) Consider a swing on which a child sits. 2) When the swing is given a series of pushes by the mother of child with a frequency equal to the natural frequency of the swing, the swing oscillates with larger amplitude. 3) In this case, resonance occurs between the oscillatory force applied by the mother and the swing.

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3. Distinguish between progressive and stationary waves. (T.Q.) (March ‘09, ‘02 June 12, ‘01)

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4. Describe a method to determine the ye1ocjy of sound in air. (June ‘06, ‘05, ‘04, ‘00) (T.Q.) A. Experimental arrangement to determine the velocity or sound in air:

1) Take a long glass jar ’J’. Pour water into the jar to about, 3/4 level. 2)Take another glass tube ‘V with its both ends open and fix it to a retort stand RZ Immerse the tube Tin the water jar J. 3) The length of the air column (1) can be varied by raising or lowering ‘V using the screw 15! Adjust the position of the tube such that the length of air column is very small. 4) Take a tuning fork of known frequency u. Strike it with a rubber hammer and hold it above the air column in tube ‘T’. 5) Adjust the length of the air column and repeat as above till a booming sound is heard Note this length. Let it be 6) Repeat as above till we hear a second booming sound. Mostly this can be heard at a length equal to three times the length at which the first booming sound is heard.

7) From (1)and(2)

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8) But velocity of sound Thus the velocity of sound in air can be calculated. 5. Distinguish between transverse and longitudinal waves. (V. Imp.)

6. Describe an experiment showing the formation of a standing wave. A. Experiment: 1) Consider a string attached to an electrically vibrating tuning fork. Let the other end of the string pass over a pulley and be tied to a pan with suitable weights as shown in the figure. 2) The weights provide the necessary tension in the string. 3) Then the string is called a stretched string. 4) When the tuning fork is excited, a continuous wave (instead of a pulse) travels along the stretched string. 5) When this wave meets the fixed end (pulley), it is reflected back with a phase change of it. 6) As the tuning fork continues to vibrate, continuous reflections take place at the fixed end. 7) This means that two waves, one incident and the other reflected, travel through the string simultaneously. 8) The two waves then superpose on each other. This superposition gives rise to a

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resultant wave called ‘Stationary’ or ‘Standing wave’, as shown in the figure. Definition: A stationary wave is formed when two waves of equal frequency and amplitude travel in opposite directions along the same path,

PROBLEMS 1. In a resonating air-column experiment a tuning fork of frequency 412 Hz is used. In this experiment the 1st and 2nd resonances occur when the length of the air column is 20 cm and 60 cm respectively. Find the velocity of the sound in air. (T.E.) Sol. 1) Given: Frequency u = 412 Hz, 1st length l = 20cm, 2nd length 12 = 60 cm, Velocity of sound in air v 2) Formula: v= 2u (l2—l1) 3) ..v=2x412(60—20)= 2x412x40 =32960cm/s v = 329.60 m/s.

www.gnanmantra.com 2. The distance between a node and the next antinode in a stationary wave is 10cm. Find the wavelength. (April 2008, March 2003).

Sol. 1) Given: Distance between a node and the next antinode in a stationary wave= =10 cm 2) Wavelength =?

=10 cm = 4x10=40 cm

3. In a resonating air Column experiment with a closed-end tube, first resonance occurs when the length of the air column is 10 cm. Find out the length of the air column for the occurrence of second resonance. . (March 2004) Sol. 1) Given:I1= l0cm,l2=? 2) Formula: l2=311 =3x10= 30cm. 4. The distance between two successive Antinodes is 60 cm. What is the wavelength of the wave? Sol. 1) Given: Distance between two successive antinodes=

=60 cm

2) Wavelength=? 3)

=60 cm(or) =2x60=120cm

5. The wavelength of a stationary wave is 200 cm. Find the distance between a) Two successive nodes. b) Node and the next antinode.

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Sol. 1) Given: Wavelength (

) = 200 cm.

2) Distance between two successive nodes=

=100cm

3) Distance between the node and the next antinode=

=50 cm

6 The distance between a node and the next antinode is 25cm. What is the wavelength of the wave?

Sot 1) Given: 2)

=4x25=100cm

7. The wavelength of a stationary wave is 400 cm. What is the distance between two successive antinodes? Sol. 1) Given:

= 400cm

2) Distance between two successive antinodes=

= 200 cm.

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Diagrams 1. Draw figures to indicate the first and second modes of resonating air-column in a closed tube.

First mode

Second mode

Resonating air â&#x20AC;&#x201C; columns 2. Draw a neat sketch showing the formation of a stationary (standing)wave. (Oct. 1999)

Formation of a standing wave Parts:1. Electrically vibrating tuning fork

2. Pulley

3. Loop

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3. Draw the diagram showing the position of nodes and antinodes in a standing wave.

Parts: 1. Complete P.R 2. Complete K.E 3. Complete P.R. 4. Loop N - positions of nodes AN- positions of antinode

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UNIT-7 LIGHTNATURE OF LIGHT AND SOURCES OF LIGHT

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INTRODUCTION Light is a form of radiant energy or energy that travels in waves. Since Greek times, scientist has debated the nature of light. It is said that light is a form o particles. When moving place to place, light acts like a system of waves. All light can be traced to certain energy sources, like the sun , an electric bulb or a match stick when light travels through the material it reflects back or bounces back if the material is not opaque, the light goes through it at a slow speed and it is refracted or bent like how it happened in a water. Light wave is also formed into other sources of every such as heat energy etc. the light wave makes electrons vibrate and this kinetic energy or movement energy makes heat. Light also have different colors, when light starts to travels in different wavelength region forms different colors and using different source .Here we are going to discuss about the visible light. This is an electromagnetic radiation that is visible to human eye. Visible light having wavelength in range 400nm or 400*10-9m .so we will have various theory of light and its properties.

HISTORY: There was a great conflicting understanding between the inventors that some says that light is a form of wave, and some says that light has tiny particles called corpuscles . , One of the first people to have studied the nature of light was Sir Isaac Newton. in 17th century he studied that light as a corpuscular , that means light is made of tiny particles called corpuscles ,

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Newton’s view on the light was accepted by many scientist and followed over 100 years Thomas young and Francesco girmaldi had given a huge blow to Newton’s view on the light when they allowed light to pass through a narrow slit when light started to bend , where the light t doesn’t have such properties being a particle to bent , so Huygens wave theory was later discovered by Huygens who state that light is form of wave In the 19th century James clerk Maxwell came with a brilliant equation saying that electricity and mathematics’ are linked to each other , he also stated that there should be a kind of wave that make both inter locked making a pattern of oscillating electric and magnetic field At last it was the found that electromagnetic field was existed In 1899, Phillip Leonard explained that the negatively charged particle beam consisted of electrons which were already discovered by J. J THOMPSON. The first person to give a solution to the problem of black body radiation was maxplank who in 1900 suggested that form of quantanization that accelerating predicted the results for t black body radiation. Einstein was recommended to work on light by maxplanck in Prussian academy. And tried to proved that light has particles which was later accepted when Compton an American physicist has worked out on light independently In this way many involved in the invention of light and proved that light is form of wave which contained particles called corpuscles

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SCIENTIST INFORMATION

Christian Huygens (14 April 1629 â&#x20AC;&#x201C; 8 July 1695) was a prominent Dutch mathematician and natural philosopher. He is known particularly as an astronomer, physicist, probabilistic and horologist. Christian Huygens was born in 14 April 1629 at The Hague, in a rich and influential Dutch family, [3] [4] the second son of Constantijin Huygens. Christian was named after his paternal grandfather. [5][6] His mother was Suzanna van Baerle. She died in 1637, shortly after the birth of Huygens' sister In 1644 Huygens had as his mathematical tutor Jan Jansz de Jonge Stampioen, who set the 15-year-old a demanding reading list on contemporary science.[11] Descartes was impressed by his skills in geometry His father sent Huygens to study law and mathematics at the University of Leiden, where he studied from May 1645 to March 1647.After two years, from March 1647, Huygens continued his studies at the newly founded College of Orange, in Breda, where his father was a curator: the change occurred because of a duel between his brother Lodewijk and another student In 1654, Huygens returned to his father's house in The Hague, and was able to devote himself entirely to research. The first work Huygens put in print was Theoremata de quadratura (1651) in the field of quadrature. It included material discussed with Mersenne

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some years before, such as the fallacious nature of the squaring of the circle by Grégoire de Saint-Vincent. His preferred methods were those of Archimedes and Fermat. [14] Quadrature was a live issue in the 1650s, and through Mylon, Huygens intervened in the discussion of the mathematics of Thomas Hobbes. Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation Huygens is remembered especially for his wave theory of light, which he first communicated in 1678 to the Paris Académie des sciences. It was published in 1690 in his Traité de la lumière (Treatise on light).[79] He refers to Ignace-Gaston Pardies, whose manuscript on optics helped him on his wave theory Huygens investigated the use of lenses in projectors. He is credited as the inventor of the magic lantern, described in correspondence of 1659.He died in The Hague on 8 July 1695, and was buried in the Grote Kerk.[60]

USES OF LIGHT : In this world to see everything visible and clear we need light  Light is essential to identify the colors , without which it doesn’t happen  To see the colors  Light is used for human on the earth during the night time to clearly or else the night would have be left dark  House appliance need light , cars and motors vehicles also need light APPLICATION OF LASER LIGHT Laser is use in many fields as follows IN SCIENCE AND TECHNOLOGY :  LASER was successfully used to separate isotopic species in a substance containing mixture of isotopic element

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 Laser is employed in a 3Dpotography called holography  A new branch called atmosphere optics uses laser to measure pollution gases and other contamination . IN MEICINE :  Laser is used for bloodless surgery , the liver and lung diseases can be treated by laser  Laser are used in fibre optic endoscope to detect ulcers in the intestine IN INDUSTRY :  Laser are used in for cutting drilling and welding of metals and other materials  Laser is used to detect the bar code printed n the products IN DEFENCE AND SPACE Research :  Laser are used in various guide missiles and for detection of every targets  Laser are also used in space for communication in radars and satellites

BASIC CONCEPTS OF LIGHT : In this chapter we are going to discuss about the light theory discovered by Newton and Huygens NEWTONS CORPUSCULAR THEORY :  Sir Isaac Newton was the first person to study the nature of the light in the mid of 17th century  According to this theory light contains tiny elastic particles called corpuscles

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 These corpuscles are emitted by a luminous source like sun , candle , electric lamp ,etc .  These corpuscles travel in a straight line  The velocity of corpuscles are different from each other  The corpucsles are different in size and various colors due to different in their size .  The reflection and refraction of light are explained by the repulsion and attraction of the corpuscles by the medium  It can explain the phenomena of interference, diffraction and polarization of light

HUYGENS WAVE THEORY : A duchist Christian Huygens (1678) assumed that light travels in the form wave from a source . This is called wave theory of light . “ Huygens principle sates that every point in the wave front behave like a source of small secondary wavelets which spread out in all direction with a velocity equal to the velocity of the light .the new wave front is then framed by constructing a tangential surface to the secondary wavelets .  It assume that light travels in the form of wave  The rectilinear propagation of wave is advancement of wave front alining the direction of normal drawn to it  The colors of the light is due to difference in the wavelength  the reflection and refraction of light is explained by the construction of secondary wave fronts applying Huygens principle  It can explain the phenomena of interference, diffraction and polarization of light  It correctly proves that velocity of light in denser medium is less than that in a rarer medium

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VISUAL PHOTOMETRY :visual photometry is the science of measuring the brightness or relative luminous intensities of light emitted by different source using standard and techniques

LUMINIUS FLUX : It is the amount of radiant energy flowing from a source of light per unit time and is expressed in ergs per second

LUMINIOUS INTENSITY : It is a point source of light is defined as the luminous flux emitted it per unit solid angle

SOLID ANGLE : ratio of the area of conical surface to the square of the radius of the sphere

CANDELA : it is the 1/60th square centimeter area of the luminous intensity CANDLE POWER : Its is a source in luminous intensity in a given direction expressed in candela.

LASER It is the important part of the study of light so let us some basic of laser light LASER : The basic information on laser was put forth by Dr. Charles H Townes in 1954. The efforts of several scientists later led to the development of the first laser called pulsed laser in 1960 The word LASER is abbreviated as LIGHT AMPLIFICATION BY STIMULATED EMMISION OF RADIATION . LASER is a simple source of light but has some extra ordinary properties THE FOUR MAIN PROPERTIES OF LASER: the four main properties of laser are COHERENCE : IN laser the process of electronic transition takes place in an orderly manner and the phase relation is consistent and does not change . Their phenomenon is called as temporal coherence DIRECTIONALITY : visible light travels in all the direction but a laser light travels in a single line without any divergence MONOCHRMACITYT: LASER light has the nature of monochrmoacity that is it has a single color and single wave length INTENSITY : Intensity is the energy of wave per unit time flowing through a normal area

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IMPORTANT POINTS  According to Newton’s corpuscular theory, light consists of a stream of tiny, light and perfectly elastic particles called corpuscles.  The velocity of light is different in different media. According to the corpuscular theory of light, various colors of light are supposed to be due to different sizes of corpuscles.  Corpuscular theory could not explain the phenomena of interference, diffraction and polarisation of light.  According to Huygens’ theory, light travels in the form of waves.  The basis of Huygens’ wave theory of light is his principle concerning construction of wave front.  Huygens’ principle states that every point on a wave front behaves as the source of small secondary wavelets which, spread out in all directions with a velocity equal to the velocity of light. The new wave front is then found by constructing a surface of envelope tangential to the secondary wavelets.  Applying Huygens’ principle, the phenomenon of reflection and refraction could be explained.  The velocity of water waves depend on the depth of the water.  Interference: If the two sources vibrate with same frequency and amplitude, the superposition of waves from them results in well defined maxima or minima in space. The physical effect observed as a result is called interference.  The formation of antinodal and nodal lines results in relatively bright and dark regions called interference pattern of waves.  Interference ft not limited to water waves but is a characteristic phenomenon of all waves including light waves.  Diffraction: The bending of a wavefront or its deviation from its original direction of propagation when it meets a small obstacle is called diffraction.  The bending of light waves around an obstacle whose dimensions are comparable to the wavelength of the incident light and hence its spreading into the geometrical shadow is called diffraction.

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PREVIOUS EXAMINATION QUESTIONS 1. Give a comparison between Newtons Corpuscular Theory and Wave Theory. (March 2012, 2010, ‘05, ‘03, October ‘99, April ‘08, June 2008) 2. Describe a Ripple Tank. How does it help in understanding reflection and refraction of light? (June 2007, March 2002, 1999) 3. Explain the phenomenon of reflection applying wave theory of light. (June 2001) 4. Describe the diffraction of light waves at an aperture with a neat diagram. (June00)

Short Answer Questions 1. What are the different theories which explain the nature of light? A. The different theories that explain the nature of light are 1) Newtons corpuscular theory 2) Huygens’ wave theory. 3) Maxwells electromagnetic theory.

Very Short Answer Questions 1.What is interference? (T.Q.) A. The physical effect of super position of waves from two sources vibrating with same frequency and amplitude is called the interference of waves. 2. What is diffraction? (T.Q.) A. The bending of a wave or its deviation from the original direction of propagation when it meets a small obstacle is called diffraction. 3. What is a plane wavefront? A. ‘A small portion of a spherical (or) cylindrical wave front originating from a source at a large distance will appear as plane. This plane is called a plane wavefront. 4. What is a light ray? A. ‘An imaginary line drawn normal to any wavefront represents the path along which light travels. This path is called a light ray’.

www.gnanmantra.com 5. What is the law of reflection of light? A. â&#x20AC;&#x2DC;A plane Wave is reflected from a plane surface such that the angle of reflection is equal to the angle of Incidenceâ&#x20AC;&#x2122;. 6. State the principle of super position of waves. A. Principle of super position of waves. The principle of super position of waves states that when two or more waves travel through the same portion of a medium simultaneously, the resultant displacement at any point is the vector sum of the displacements due to individual waves. 7. What are the various properties of light? A: The various properties of light are 1) Reflection 2)Refraction 3) Interference 4) Diffraction 5) Polarisation. 8. What is constructive super position? A. When two waves vibrate with same amplitude such that crest falls on crest or trough falls on trough, a maximum displacement is produced. This condition of super position is called constructive super position. 9. What is meant by destructive super position? A. When two waves vibrate with same amplitudes such that crest falls on trough or trough falls on crest. a minimum or zero displacement is produced. This condition of super position is called destructive super position.

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Long Answer Questions 1. What is the basis of Newton’s corpuscular theory of light? What are its assumptions? (T.Q.) A. Light consists of a stream of tiny, light and perfectly elastic particles called corpuscles’. Assumptions: 1) These corpuscles are emitted by a luminous sources like sun, candle, electric lamp etc. 2) The corpuscles travel in all directions in straight lines. 3) The velocity of corpuscles is different for different dispersive media. 4) When these corpuscles fall on the retina of the eye, they cause the sensation of vision. 5) The corpuscles can be of different sizes and the various colors of light are supposed to be due to difference in their sizes. 2. How do you-explain the reflection and refraction of light by corpuscular theory? A. - Reflection of light: 1) The reflection of light is explained by the corpuscular theory in exactly the same way as the reflection of a perfectly elastic ball from a rigid plane. 2) See figure. The corpuscles are repelled near the reflecting surface in such a way that angle of incidence 0) is equal to the angle of reflection (r). Refraction of light: 1) According to Newton, when corpuscles of light approach-a refracting surface, they are attracted near the surface. 2) When they enter the denser (say 2) from a rarer medium (say 1) their speed increases and hence changes their direction. See figure. –

www.gnanmantra.com 3. What is the basis of Huygens’ wave theory of light? What are its assumptions? (T.Q.) A. Huygens’ wave theory: 1) A Dutch physicist Christian Huygens (1678) assumed that light travels in the form of waves from-a source. This is called ‘wave theory of light. 2) The basis of Huygens wave theory of light is his principle concerning construction of wavefront. Assumptions: 1) The propagation of a light wave requires a material medium. According to Huygens, the medium is an all pervading, subtle and elastic hypothetical medium called ‘either’. 2) A luminous source sends out light energy uniformly in all directions, causing disturbance in the surrounding ether medium. 3) These disturbances travel through ether in the form of longitudinal mechanical waves. 4. Explain the concept of a wavefront and hence alight ray. (T.Q.) A. Wavefront- concept: 1) When a disturbance from a light source travels into ether medium in all three dimensions, the particles of the medium at different distances from the source will be vibrating in different phases. 2) If we join all those particles which are in the same phase of vibration, we get a surface which represents a wavefront. 3) The imaginary three dimensional surface formed by the envelope of all those particles of medium which are vibrating in the same phase is called a wavefront. Light ray An imaginary line drawn normal to the wavefront represents the path along which the light wave travels. The path is called a light ray.

www.gnanmantra.com 5. State and explain the Huygens’ principle. (T.Q.) A. Huygens’ principle: Huygens’ principle states that every point of a wavefront behaves as the source of small secondary wavelets which spread out in all directions with a velocity equal to the velocity of light. The new wavefront is then found by constructing a surface tangential to the secondary wavelets. Explanation: 1) Consider a point source of light S. It sends out spherical wavefronts around it, as shown in the Fig. Let AB represent a spherical wavefront at any instant. Let us find its position after time ‘t seconds.. 2) According to Huygen’s principle each point on this AB acts as a source of light called secondary source. 3) The light emerges from these secondary sources (such as 1 2, 3 ) again as small spheres called wavelets. 4) The radius of each of these spheres is given by ct, where c is the velocity of light. 5) A surface tangential to all these wavelets gives an envelope CD. This CD gives the new position of the wavefront AB after a time interval’s. 6) This process of construction of new wavefronts at different position can be continued 7) Thus light advances in a direction perpendicular to the wavefront. This method of construction of wavefronts is the essence of the Huygens’ principle. 6. Is Huygens’ wave theory correct in all respects? What modifications were necessary to explain the phenomenon of interference and diffraction? (T.Q.) A. 1) it should be noted that the Huygens’ theory assumes simply that light energy is propagated as a wave motion. 2) At the time of his proposition, Huygens did not have any idea about wavelength or about the trans-verse nature of light. 3) The Huygens’ wave theory was later modified by Thomas Young and Fresnel.

www.gnanmantra.com 4) They introduced the concept of wavelength and assumed that light waves are transverse. 5) By these assumptions they could successfully explain not only the rectilinear propagation of light but also the phenomena of interference,, diffraction and polarisation of light. 6) Further, wave theory of light could prove that the velocity in a denser medium is less than that in a rarer medium. 7. Give a comparison between Newtonâ&#x20AC;&#x2122;s corpuscular theory and Huygensâ&#x20AC;&#x2122; wave theory. (June 08, April 08, March 12, 11, 10, 05, 03, Oct. 99)

www.gnanmantra.com 8. Describe a Ripple tank. How does it help in understanding reflection and refraction of light? (T.Q.) (June ‘07, March ‘02, ‘99) A.1) The ripple tank essentially consists of a rectangular shaped tank made of transparent glass. This tank containing water is held at a height with the support from four legs. 2) Below the tank, a white paper is spread on the floor. Above the-tank, a partially covered electric-bulb is fixed to illuminate the tank. 3) A small needle (N) is fixed at one end of a metallic strip connected to an electric vibrator. The tip of the needle is kept vertically in contact with the water surface in the ripple tank. 4) When the strip vibrates, the needle also vibrates and produces disturbance. This disturbance travels in the water in the form of circular waves with the tip as the centre. Reflection of waves in a Ripple Tank: 1) A circular water wave produced by the vibrating tip of the needle in the ripple tank travels forward. Such circular waves with origin at S are shown in the figure. 2) When such circular waves with S (source) as the center move forward and meet an obstacle like the vertical flat wall (AB) of the ripple tank. 3) They change their direction of motion and start moving in the opposite direction . These reflected waves are also circular in shape. Refraction of waves: 1) In a ripple tank two regions (A and B) can be created by introducing a pile of glass plates in region B. 2) Thus, region ‘B’ is a shallow water region while region ‘A’ is a deep water region. 3) Thus, the two regions behave as two media for water waves. 4) It is known that deeper the water, higher the velocity of waves. So the refraction of light appears as in the figure given below.

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9. Explain the formation of bright and dark bands on the paper below the ripple tank. (T.Q.) A. Formation of bright and dark bands: 1) The crest of the water wave behaves as a convex lens and the trough as a concave lens. 2) The light incident on the tank therefore is transmitted on to the paper on the floor differently by crests and troughs. 3) In the case of a crest, the light converges and forms a bright band as shown in the figure. 4) In the case of a trough, the light diverges and forms a dark band. 5) Thus, a light pattern consisting of successive bright and dark bands can be seen on the paper below the ripple tank. The pattern represents the water waves in the ripple tank.

www.gnanmantra.com 10. State and explain the principle of superposition of waves. (T.Q.) A. 1) Principle of superposition of waves (statement): The principle of superposition of waves states that when two or more waves travel through the same portion of a medium simultaneously, the resultant displacement at any point is the vector sum of the displacements due to individual waves. 2) Explanation: a) The resultant displacement / at the point (R) = Y1 + Y2. b) Y1 is the displacement caused at the point due to first source. c) Y2 is the displacement caused at the point due to second source. 3) If the two sources vibrate with the same amplitude, then Yi = Y2 = Y. 4) The resultant displacement will be maximum and R = t = Y + Y = 2Y. 5) In the case of destructive superposition, the resultant displacement will be minimum and R=Y1â&#x20AC;&#x201D;Y2=Yâ&#x20AC;&#x201D;Y=O. 11. When do we get constructive and destructive superposition of waves?(T.Q.) A. Constructive and destructive superposition of waves:

1) In the case of a ripple tank with two vibrating sources, if Yi is the displacement caused at a point due to first source and Y2 is the displacement at the same point due to the second source, the resultant displacement (R) at that point is given by

www.gnanmantra.com R=Y1+Y2 (1) When the two sources vibrate, with same amplitude, then Yi and Y2 are each equal to Y. 2) In eq. (1), if Yi is due to the crest (or trough) and Y2 is also due to crest (or trough) of the waves, the resultant displacement will be maximum and R Y1 + = Y + Y = 2Y (constructive superposition) (2) 3) Thus, when crest falls on crest or trough falls on’ trough as shown in Fig. (a), a maximum displacement (solid curve) is produced. 4) When such maximum displacement occurs, the waves are said to superpose constructively. 5) ‘Thus, constructive superposition is obtained between two waves when phase difference between them at the point is zero or an integral multiple of 2it i.e., 2itn, where n=O, 1, 2, 3 6) On the other hand, if Y1 is due to the crest of the first wave andY2 is due to the trough of the second wave, the resultant displacement will be minimum and R = Y1 — Y2 = minimum (destructive superposition) (3) In the special case where Y1 = Y2 = Y, R = 0 (destructive superposition) 7) Thus, when crest falls on trough or vice versa, as shown in Fig (b) a minimum displacement (solid curve) is produced. 8) When such minimum displacement occurs, the waves are said to superpose destructively. Thus, destructive superposition is obtained between two waves when phase difference between them at the point is it or integral multiple of it i.e., nit, where n = 1, 2, 3….

12. Explain how the phenomenon of interference of water wave’s can be demonstrated in a ripple tank. What are nodal and antinodal lines? (T.Q.) A. 1) The interference of water waves .in a shallow ripple tank can be produced if we take two identical adjacent pins 51 andS2 vibrating, with the same frequency. When the pins vibrate waves are produced and spread into all the possible directions and interfere.

www.gnanmantra.com 2) Under the illumination of the ripple tank, anâ&#x20AC;&#x2122; interference pattern is observed on white paper spread below the tank. In the figure crests are shown by solid lines and trough with dotted lines. 3) Consider a point A, Here the crest of a wave falls on crest of another wave similarly at point B, Superposition of two troughs takes place. 4) Thus at both points A & B, maximum disturbance occurs and the superposition is therefore a constructive super position. The points like A and B will appear relatively bright on the paper. 5) Consider the points C and D. Here crest of a wave is superposed on the trough of another. Thus at the points C and D, destructive superposition occurs and they appear relatively dark on the paper. . 6) All the points like A, B fall on a line called antinodal line meaning maximum disturbance. 7) All the points like C, D fall on the line called nodal line meaning minimum disturbance. 8) The formation of antinodal and nodal lines results in relatively bright and dark regions called interference pattern of waves. 13. Explain the diffraction of water waves in a ripple tank at an aperture. (T.Q.) A. Diffraction of water waves at an aperture: 1) Let the tip S) of the needle connected to the electrical vibrator produce circular wavefronts travelling along (P) and X, Y be two vertical glass plates immersed in the tank far away from the vibrating source 5, such that there is an opening AB between them. 2) Then, a plane wavefront MN would be incident on AB where the edges A and B act as obstacles. Any opening such as AB is called an â&#x20AC;&#x2DC;apertureâ&#x20AC;&#x2122;. 3) The portion of the wavefront incident on AB-escapes through the aperture and results in a number of circular wavefronts which spread out in all directions as if

www.gnanmantra.com they have originated in the aperture AB. 4) The waves emerging from AB deviate from their original direction of propagation along ‘F’ and travel along other directions like Q and R: 5) The formation of circular wavefronts and their propagation in a direction different from the original direction is due to bending’ of the waves. This phenomenon is called ‘diffraction.’

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7.5 VISUAL PHOTOMETRY 7.6 LASER- A SPECTAUCULAR LIGHT

IMPORTANT POINTS  Visual photometry is the science of measuring relative intensities of light emitted by different sources using certain standards and techniques.  Luminous flux or light flux is the amount of radiant (light) energy flowing from a source of light per unit time and is expressed in ergs per second. But, it is measured in lumens.  Luminous flux depends on ‘illuminating power’ or ‘luminous intensity’ of the light source.  Solid angle is defined as the ratio of the area of the surface of the portion of a sphere enclosed by the conical surface forming the angle, to the square of the radius of the sphere.  The total solid angle for the sphere as a whole, is given by . sr.  Luminous intensity or illuminating power (J) of a point source of light is defined as the luminous flux emitted from it per unit solid angle. It is measured in units of candela (cd).  Candela (cd) is defined as the luminous flux emitted pet unit solid angle along normal to the surface by one sixtieth (1/60) square cm. area of a black - body radiator kept at the temperature 2046 K of solidifying platinum.

www.gnanmantra.com  The luminous flux of a light source is measured in the units of LUMEN (lm).  Lumen (lm) is the amount of light emitted per second by uniform (point) source of one candela within a cone of unit solid angle.  A source having an illuminating power of 1 candela is said to be of 1 candle power.  A light source is said to be of unit illuminating power or unit luminous intensity if it radiates a flux of 1 lumen through a unit solid angle.  ICBM: Inter Continental Ballistic Missile.  LASER: Light Amplification by Stimulated Emission of Radiation.  Laser light is distinguished from an ordinary light source by its (1) coherence, (2) directionality (3) monochromaticity and (4) high intensity.  Lack of coherence makes ordinary light an optical noise.  Coherence makes a laser light ‘optical music’.  The directionality, of laser enables us to focus the light to a point on a target at large distance.  Light from sodium lamp is monochromatic.  In the working of- laser, the atomic processes (i) absorption, (ii) spontaneous emission, (iii) stimulated emission of electromagnetic radiation; take place.  The process in which number of electrons (N2) in a higher energy state called metastable state of an active medium is increased to a. value greater than the number (N1) in the ground state (i.e., N2 > N1) is called ‘population inversion’.  The process of achieving ‘population inversion’ is called PUMPING.

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PREVIOUS EXAMINATION QUESTIONS 1. Compare the intensities of an ordinary light and laser light. (March 1999) 2. What are the basic processes involved in the working of a laser? (March 2001) 3. Mention the uses of lasers in industry. (March 2008, June 2006, 2003) 4. Give the applications of lasers in the field of medicine. (March ‘09, ‘08, June 06) 5. How do you distinguish LASER light from an ordinary light in terms of the propert9 of ‘coherence’? (March 1999) 6. What are the uses of lasers in Defence and Space Science? (March 2008) 7. What are the important applications of laser in science and technology? (March ‘06, ‘04, June ‘04, ‘02) 8. Describe the actual laser and its working. (or) What are the main parts of an actual laser? (March ‘07)

Short Answer Questions 1. Explain the terms luminous flux and luminous Intensity. Give their units. (T.Q.) A. Luminous Flux: The amount of radiant (light) energy following from a source of light per unit time is called luminous flux or light flux. It is measured in lumens. Luminous Intensity: Luminous intensity of a point source of light is defined as the luminous flux emitted from it per unit solid angle. It is otherwise called Illuminating power (I). If is measured in candela (cd). 2. What are the special properties of a laser light? (T.Q.) A. The special properties of LASER Light are: (1) Coherence (2) Directionality (3) Monochromaticity (4) High intensity.

www.gnanmantra.com 3. Explain coherence. (T.Q.) A. Coherence: 1) Visible light energy is emitted when the excited electrons iii atoms undergo transitions to the ground state. 2) In ordinary light sources, these transitions take place at random in time and the light waves received at a point on a screen bear no definite phase relation among them. 3) But, in a laser source, electronic transitions take place in an ‘orderly way and the light waves emitted have a consistent phase relation which does not change with time. 4) This is called temporal coherence’ and is the most important characteristic of laser light. 4. Explain the property of the directionality of a laser. (T.Q.) A. Directionality: 1) The conventional sources like lamp, torch light and sodium lamp emit light in all directions. This is called divergence. Laser, on the other hand, emits light only in one direction. This is called ‘directionality’ of laser light. 2) Take the example of a powerful search light. If the beam from it travels a distance of 1 km, it spreads to about a kilometer in diameter. 3) If a laser travels a distance of 1 km, it spreads to a diameter less than 1 cm. 4) The directionality of laser enables us to focus the light to a point on a target at large distance. 5. What do you mean by ‘monochromaticity’ of a laser beam? (T.Q.) A. Monochromaticity: 1) Light from sodium lamp is monochromatic i.e., of single colour or of single wavelength of about 5893 A. When we say that the wavelength of sodium light is 5893 A, it means simply that intensity is maximum at this value. 2) However, intensity is not zero for wavelengths above and below 5893 A up to even 500 A on either side. This spread of wavelength (or frequency) about the wavelength of maximum intensity is called ‘band width’ (or range).

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4) Because of this monochromaticity, large energy can be concentrated into an extremely small band width. 6. Compare, the intensities of an ordinary light and laser light.(Mar 99)(T.Q.)

7. What are the basic processes involved in the working of a laser? (T.Q.) (March 2001) A. The basic processes involved iii the working of a laser are: 1) Absorption, 2) Spontaneous emission, 3) Pumping and population inversion. 4) Stimulated-emission of electromagnetic radiation. 8. Distinguish between spontaneous emission and stimulated emission of radiation. (T.Q.)

www.gnanmantra.com 9. What are the main parts of an actual laser? (T.Q.) A. The main parts of an actual laser are 1) The active medium (A) which is placed in a special cell called cavity resonator (R). 2) Two partly reflecting mirrors M and M2 which are arranged at each end of the resonator. 3) External light source. 10. Mention the uses of lasers in industry. (June 10, Mar 08, June 06, 03) (T.Q.) A. Lasers in industry: 1) Lasers are used now for cutting, drilling and welding of metals and other materials. 2) Laser light is used to collect the information about the prefixed prices of various products in shops and business establishments from the bar-code printed on the product. 11. Give the applications of men in the field of medicine. (March’09, ‘08, June’12, ‘10, ‘06) (T.Q.) A. Lasers in Medicine: 1) .Lasers are used or bloodless surgery. 2) The liver and lung diseases could be treated by lasers. 3) Lasers are used in fiber-optic endoscope to detect ulcers in the intestines. 4) Lasers are used extensively in the treatment of eye-diseases, particularly to reattach a detached retina. 12. How do you distinguish LASER light from an ordinary light in terms of the property of ‘coherence’? (March 1999) A. 1) Visible light energy is emitted when the excited electrons in atoms undergo transitions to the ground state. These transitions take place at random in time and the light waves received at a point on a screen bear no definite phase relation among them. So incoherence or optical noise is the character of ordinary light. 2) In LASER light electronic transitions take place ‘in an orderly way and the light waves emitted have a consistent phase relation which does not change with time. This is called ‘temporal coherence’ or optical music’ is the characteristic of LASER light.

www.gnanmantra.com 13. What are the uses of lasers in Defence and Space Science?(Jun ‘10, Mar ‘08) (T.Q.)

A. Lasers in Defense and Space Science: 1) Lasers are used in various guided missiles and also for detection of enemy targets. 2) Lasers are also used in space communication, in radars and in satellites. Compare the intensities of an ordinary light and laser light. 14. Compare the intensities of an ordinary light and laser light.

15. What are the main differences between laser and other sources of light? A. Laser light is distinguished from an ordinary source of light by four characteristic and striking properties. These are 1) coherence 2) directionality 3) monochromaticity and 4) high intensity. 16. Distinguish between ‘Divergence’ and ‘Directionality’.

17. Distinguish between a search light and laser I terms of spreading.

18. Distinguish between ordinary monochromatic light and laser with reference to bandwidth.

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Very Short Answer Questions 1. What is Visual photometry? (T.Q.) A. The branch of science which deals with measurement of brightness or luminous intensities of light emitted by different sources using certain standards and techniques is called visual photometry. 2. Define Solid angle. (T.Q.) A. The ratio of the area of the surface of the portion of a sphere enclosed by the conical surface forming the angle to the square 0 the radius of the sphere is called solid angle. 3. What is a Lumen? (T.Q.) A. Lumen is the amount of light energy emitted per second by a uniform (point) source of one candela within a cone of unit solid angle 4. Define Candela. (T.Q.) A. Candela is defined as the luminous flux emitted per unit solid angle along normal to the surface by one sixtieth (1/60) square cm area of a black body radiator (source) kept at the temperature of solidifying platinum. 5. What is Population inversion? (T.Q.) A. The process in which number of electrons (N2) in a higher energy state called metastable state of an active medium is increased to a value greater than the number (N1) in the ground state (i.e., N2 > N1) is called population inversion. 6. Define Candle power. A. Candle power of a light source, in a given direction is the luminous intensity of the source in that direction expressed in terms of candela. 7. What is the full form of LASER? A. The full form of LASER is Light Amplification by Stimulated Emission of Radiation.

www.gnanmantra.com 8. What is Pumping? A. The process of achieving population inversion is called Pumping. 9. What are Active systems or Active media? A. There are certain special substances or systems in which electrons once excited can remain in the higher energy state for longer time. Such systems or substances are called Active systems or Active media. 10. What are various types of lesers? A. Various types of lasers can be broadly classified into: 1) Solid state laser 2) Liquid and dye lasers 3) gaseous lasers. 11. What is meant by temporal coherence? A. Temporal coherence: When the light waves emitted have consistant phase relation which does not change with time, they are said to be in temporal coherence. 12. Define band width. . A. Band width: The spread of wavelength about the wave length of maximum intensity is called band width. 13. What is meant by metastable state? A.. The state of electrons in higher energy level in which the life time of the electrons is 3 x 10-s seconds, then such state is called meta stable state. 14. What is meant by intensity of a wave? A. The intensity of a wave is the energy per unit time flowing through a unit normal area.

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Long Answer Questions 1. What are the important applications of laser in science and technology? (T.Q.) (March 2013, 2006, 2004, June 2004, 2002) A. Science and Technology: Lasers help in understanding and offering clarifications for many basic problems of science and technology. 1) It helps in studying the Brownian motion of particles. 2) With the help of He - Ne laser, it was proved that the velocity of light is same in all directions. 3) He - Ne laser helped in determining the rate of rotation of the earth accurately. 4) The counting of atoms in a substance became possible because of a laser. 5) Lasers have been used successfully to separate isotopic species in a substance containing mixture of isotopes of an element. 6) Lasers have been used to study the nature of plasma state of matter and also to achieve high temperatures necessary to cause thermonuclear fusion of atoms. 7) Lasers are employed in a special three dimensional photography called ‘holography’. 8) In astronomy, lasers helped in extending the distance of observation of stellar objects and study their nature. 9) The high intensity and directionality of lasers led to the development of a new. branch of science called micro-Raman spectroscopy which analyses small quantities of biological and biomedical samples. 10) In computers, lasers are used to retrieve stored information from a compact disc (CD). 11) It is the development of lasers which helped in establishing a new revolutionary method of communications called ‘fibre-optic communication’. 12) A new branch called ‘Atmospheric Optics’ uses lasers to measure, pollutant gases and other contaminants of the atmosphere.

www.gnanmantra.com 2. Describe the actual laser and its working. (or) What are the main parts of an actual laser? (March 2007) A. Actual laser and its working:

1) An actual laser consists of the active medium (A) in a special cell called cavity resonator, R. 2) Two partly reflecting, mirrors Mi and M2 are arranged at each end of the resonator as shown in Fig. 3) The light generated within the active medium A is made to bounce back and forth in the resonator. 4) This stimulates other atoms so that they too emit identical light. 5) This amplified light escapes through the partly reflecting mirror. 6) The intense flash of light that emerges is our laser beam. In Fig. E is the external light source which causes pumpingâ&#x20AC;&#x2122;. 3. Compare the intensities of an ordinary and laser light. A. The light from an ordinary source spreads out uniformly in all directions. If we look at a 100 watt lamp filament from a distance of 30 cm the power entering the eye is less than 1/1000 watt. But in the case of laser light the energy is emanated in small region of space and in a small wavelength range and hence is said to be of great intensity. If you look directly along the beam from a laser then all the power in the laser would enter our eye. Even a 1 watt laser appear many thousand times more intense than 100 watt ordinary lamp. The intensity is so enormous, that a power of 1015 watt can be concentrated into an area of 1 sq. cm.

www.gnanmantra.com 4. What are the basic processes involved in the working of a laser? A. The basic processes involved in the working of a laser are 1) Absorption 2) Spontaneous Emission 3) Pumping and Population Inversion 4) Stimulated Emission 1) Absorption: In the absorption process, the electron in the ground state of an atom absorbs the incident energy and goes to the excited â&#x20AC;&#x2DC;state. 2) Spontaneous Emission: The process of electrons being released on their own from the excited states in an atom and emitting incoherent light is called spontaneous emission. In the spontaneous emission, electronic transitions takes place at random in time and the photons or light waves emitted have no correlation in phase. Such light is called incoherent light. 3)Pumping and Population Inversion :The processes in which the number of electrons (N2) in a higher energy state called meta stable state of an active medium is greater than the number of electrons in the ground state is called population inversion and the process of achieving population inversion, is called pumping. 4) Stimulated Emission: When an external coherent beam is incident on the active system in the population inversion, the electrons are induced or stimulated to undergo simultaneous transitions from the excited state to the ground state emitting amplified coherent radiation. This process is called stimulated emission.

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UNIT-8 MAGNESTISM

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INTRODUCTION What is magnetism? It is an invisible force that attracts certain metals, like iron. This force is something that attracts or repels an object. Any material that creates this force is called magnet. This process is called as Magnetism...magnets have two poles called North Pole and South Pole. Like pole attracts each other, unlike pole repels each other. The area around a magnet in which the object is affected by its magnetic force is called magnetic field. Scientist believes that earth has a magnetic field in its core due to which the gravitation force acts on it. Earth is actually a huge big magnet. It also has north and South Pole as a bar magnet. a bar magnet is freely suspended it shows same direction towards north pole â&#x20AC;&#x201C; south pole due to earthâ&#x20AC;&#x2122;s magnetic field. More than 2000yrs ago, the Greeks discovered some minerals that attracted things made of iron, because this thing is found in part of turkey it is called magnetism, the Greeks called it magnetite, commonly called as magnet. The most commonly used device in magnets is a compass which is used in many field such as navigation, mapping, digging, coal mines also used in finding routes with help of north-south pole direction. The natural magnet on the earth was iron magnet, but Edmond Halley a great physicist was surprised how iron magnet can be producing such charges. He proposed a theory which stated that the earth contained a number of spherical shells, one inside the other each magnetized differently slowly relating to each other.

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BRIEF HISTORY The history of magnetism first starts with Amber, which is a mineral around 600BC.Greek philosopher Aristotle Phenomenon, was aware of penile property of Amber. When rubbed with a piece of fir Amber develops ability to attracts small piece of material such as features for centuries it remained a mystery that Amber only possessed this property In 1600 AD Dr William Gilbert investigated the reaction of Amber and first recorded the word electric in a report on the theory of magnetism. According to Greeks legends once a shepherd noticed that the nails of his shoes were struck to black â&#x20AC;Śâ&#x20AC;Ś. He was standing on from the magnet was assumed to magical thing for long time. As time passed William Gilbert wrote a book called Dr Magnet which was able to disprove the superstitious about Magnets. Peregrines and Gilbert Peter is credited with first attempt to separate fact from superstitious in 1267, he wrote a letter describing about Magnetic Gilbert significantly proved the understanding of magnetism. It was Gilbert who first realized that the earth was giant magnet and that magnets could be made by beating wrought iron. He also discovered that heating resulted in loss of induced magnetism. The Chinese scientist Sun Kuo(1031-1095) was the first person to write of the magnetic needle compass and that improved the accuracy of navigation. Alexander Kneecap by 1187 was the first Europe to describe the compass and its uses for navigation.

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SCIENTIST INFORMATION

WILLIAM GILBERT William Gilbert, also known as Gilberd, (24 May 1544 – 30 November 1603) was an English physician, physicist and natural philosopher. He is remembered today largely for his book 'De Magnete' (1600), and is credited as one of the originators of the term "electricity". He is regarded by some as the father of electrical engineering or electricity and magnetism. Gilbert was born in Colchester to Jerome Gilberd, a borough recorder. He was educated at St John's College, Cambridge.[2] after gaining his MD from Cambridge in 1569, and a short spell as bursar of St John's College, he left to practice medicine in London and travelled on the continent. In 1573, he was elected a Fellow of the Royal College of Physicians. In 1600 he was elected President of the College His primary scientific work—much inspired by earlier works of Robert Norman[4][5]—was De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth) published in 1600. In this work, he describes many of

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his experiments with his model Earth called the terrella. From these experiments, he concluded that the Earth was itself magnetic and that this was the reason compasses point north (previously, some believed that it was the pole star (Polaris) or a large magnetic island on the north pole that attracted the compass). He was the first to argue, correctly, that the centre of the Earth was iron, and he considered an important and related property of magnets was that they can be cut, each forming a new magnet with north and south poles. His English word "electricity" was first used in 1646 by Sir Thomas Browne, derived from Gilbert's 1600 New Latin electricus, meaning "like amber". The term had been in use since the 13th century, but Gilbert was the first to use it to mean "like amber in its attractive properties". He recognized that friction with these objects removed a so-called "effluvium", which would cause the attraction effect in returning to the object, though he did not realize that this substance (electric charge) was universal to all materials.[6] Gilbert argued that electricity and magnetism was not the same thing. For evidence, he (incorrectly) pointed out that, while electrical attraction disappeared with heat, magnetic attraction did not Gilbert's magnetism was the invisible force that many other natural philosophers, such as Kepler, seized upon, incorrectly, as governing the motions that they observed. While not attributing magnetism to attraction among the stars, Gilbert pointed out the motion of the skies was due to earth's rotation, and not the rotation of the spheres .Gilbert made the first attempt to map the surface markings on the Moon in the 1590s. His chart, made without the use of a telescope, showed outlines of dark and light patches on the moon's face. Contrary to most of his contemporaries, Gilbert believed that the light spots on the Moon were water, and the dark spots land.[8]

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Gilbert, in his work, De Magnete printed in 1600 has only some vague notions that the magnetic virtue of the earth in some way determines the direction of the earth's axis, the rate of its diurnal rotation, and that of the revolution of the moon about it Gilbert died on 30 November 1603 in London. His cause of death is thought to have been the bubonic plague.

USES OF MAGNETS Magnets are used mostly in two fields it is used in the magnetic compass to find the routes and help in navigation and used in electromagnetic field which induces the direction and flow of electricity

USES OF MAGNETIC COMPASS    

A compass can help you in navigation and in a forest a sea or in a city A compass and a map can help you out if your struck any where A captain in a ship uses compass for navigation Forest officers holds a map and compass which is mandatory for him

USES OF MAGNETS INA ELECTRO MAGNETIC FILE :  A copper wire is coiled on the magnet to prepare electric motor which transform a electrical energy into a mechanical energy or vice versa  When the device is used , current is passé through the coil the induction of magnetic field with a current causes coil to spin . to use a generator the coiled can be allowed to spin

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

In AC generators a spinning coil produces oscillating EMP at constant rate in magnetic field

USES OF MAGNET IN DAILY LIFE :    

Used in door step in modern doors Used in industries to lift heavy metals and irons Used in a compass to show the navigation Used in electric motor

MAGNETISM CONCEPTS : EWINGS MOLECULAR THEORY : The concept of magnetism of a substance in the microscopic constituent of the matter was first proposed by Weber in 1852 and was later developed by Ewing in 1890 The Ewing molecular theory states the following : He conducted an experiment using iron fillings filled in the test tube . He state that iron fillings in the in magnetized state is like an ordinary iron bar . these fillings are equivalent to the molecules of a magnetic substance In unmagnified state the molecules in the magnets are randomly distributed as N and S pole . When the molecular magnets are magnetized they are arranged in an orderly way. This order is due arrangement of N-poles on one direction an south pole toward one direction The N-pole of each molecular magnet is couple with the south pole of the next molecule .however these also contains free N-poles and S- poles . which make iron bar as a whole magnet with two N, S poles In general it is not able to achieve the whole magnets in an accurate way repeating the process can achieve the experiment prove up to the mark .

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FAILURE OF EWING MOLECULAR THEORY Ewing molecular theory was not able to explain the following The individual molecule of a magnetic substance like iron behave as a tiny magnet The individual molecule of a non magnetic substance like brass or saw dust is not magnets The substance like bismuth or copper are explained by the modern electron theory

INVERSE SQUARE LAW OF MAGNETISM : “ The inverse square law of magnetism states that the force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strength and inversely proportional to the square of the distance between them and acts along the line joining the poles “ MAGNETIC PERMABILITY : Magnetic permeability of a medium is defined as its ability to allow the magnetic lines of force to pass through it or allow itself to be influenced by the magnetic field

IMPORTANT POINTS  Magnetic substances like iron, cobalt can be made into magnets while non-magnetic substances like brass, copper etc., cannot be made into magnets.  Isolated magnetic poles do not exist.  According to Ewing theory every molecule of a magnetic substance behaves as a tiny magnet called molecular magnet.  Limit of magnetization of a substance is called magnetic saturation.  The two poles of a bar-magnet have equal pole strengths.  A magnet can be demagnetised by tapping, hammering, heating etc.  Ewing’s molecular theory failed to explain the distinction between magnetic and non- magnetic substances.

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 The ability of a pole of a magnet to attract or repel another magnetic pole is called its pole-strength.  The inverse square law of magnetism states that the force (F) of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths (m1ám2) and inversely proportional to the square of the distance (r2) between them and acts along the line joining the poles.

  Magnetic Permeability of a medium is defined as its ability to allow the magnetic lines of force to pass through it, or to allow itself to be influenced by magnetic field.  The permeability of free space  The ratio of the magnetic force in a medium to the magnetic force in free space is defined as relative permeability  The relation between absolute permeability permeability

of the medium. and relative

of a medium is

  The unit magnetic pole is that pole which repels with a force of newtons from an identical pole kept at a distance of 1 metre.  Magnetic field induction or magnetic flux density B is defined as the magnetic flux passing through a unit normal area.  Magnetic moment of a bar-magnet is measured by the product of its pole strength (m) and its magnetic length (2l).

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 Magnetic moment of a bar - magnet is given by  Magnetic Field Induction on the axial line is given by   Magnetic field induction on the equatorial line is given by   A point where the magnetic field induction (B) due to a bar magnet is equal in magnitude and opposite in direction to the horizontal component of earth’s magnetic field induction (Bo) is called a neutral point.  When N - pole of a bar magnet points towards geographical N pole o the earth, the two neutral points lie on the equatorial line of the bar-magnet such that they are equidistant from the centre of the magnet.  When S - pole of a bar-magnet points towards the geographical N pole of the earth, the two neutral points lie on the axial line of the bar-magnet such that they are equidistant from the centre of the magnet.  When neutral points are at a point on equatorial line of a bar magnet, the relation between magnetic moment of the magnet and the distance of the neutral point is  When neutral points are at a point on axial line of a bar-magnet, the relation between magnetic moment of the magnet and the distance of the neutral point is  The magnetic moment acquired by a substance per unit volume is defined as the intensity of magnetisation (I).

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 Magnetic susceptibility (x) of a substance is defined as the ratio of the intensity of the magnetisation (I) and the intensity of applied magnetic field (H).  Retentivity of a magnetic material is the property by virtue of which it retains certain amount of intensity of magnetisation even after the removal of applied magnetic field.  All materials can be grouped into Dia, Para and Ferro magnetic materials.  Diamagnetic substances are those in which the resultant magnetic moment of individual atoms is zero.  Paramagnetic substances are those in which the resultant magnetic moment of individual atoms is not zero.  Ferromagnetic substances are those in which the resultant magnetic moments of individual atoms align themselves in parallel because of a special effect present in them giving rise to spontaneous magnetisation.  The magnetic susceptibility (x) of a diamagnetic substance is small and negative, and it is small and positive for a paramagnetic substance while it is very large and positive for a ferromagnetic substance.  Air, water, bismuth, gold, alcohol, mercury and hydrogen are some of the diamagnetic substances.  Oxygen, solution of salts of nickel, manganese, aluminium, platinum and chromium are some of the paramagnetic substances.  Iron (Fe), Cobalt (Co), Nickel (Ni), Gadolinium (Gd), Platinum and Dysprosium are some of the ferromagnetic substances.  Domain in a ferromagnetic specimen is a small local region in which all the magnetic dipoles align parallel to each other giving rise to certain magnetisation within the domain.

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PREVIOUS EXAMINATION QUESTIONS 1. State and explain inverse square law of magnetism. (March 10, 09, 06, 03) 2. Compare the values of relative permeability and magnetic susceptibility of dia, para and ferromagnetic substances. (June 06, 04, March 04) 3. Draw a neat diagram of magnetic lines of force, when N-pole of a bar magnet [acing geographical north. Locate the null points . (June 05, Mar 03) 4. Draw a neat diagram of magnetic lines of force, when S-pole of a bar magnet faces geographical north. Locate the null points. (Mar 09, June 02, 01, Oct.99)

5. Define the terms a) Magnetic susceptibility b) Magnetic permeability. (March 2002) 6. What are the essentia1 ideas of the Ewings molecular theory of magnetism?What are the reasons for its failure? (March 2002) 7. Define the terms a) Magnetic susceptibility. b) Magnetic permeability. Compare the values of Relative permeability and Magnetic susceptibility of Dia, Para and Ferro magnetic substances. (March 2001) 8. State the Inverse square law of magnetism. (March ‘12, June 2000) 9. What is meant by Magnetic moment? (June 2005, 2000) 10. ‘Distinguish between Dia magnetic and Para magnetic substances. (June 2000) 12. Explain the dia, para and ferro magnetic substances. Give two examples of each type. (March 1999) 13. What is the value of magnetic induction at a distance ‘d on the (1) axial line, (2) equatorial line of a bar magnet? (March 2007) 14. Why a ferromagnetic substance like iron rod is not a magnet by itself? Explain on the basis of domain theory? (March 2008)

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15. Calculate the value of the magnetic induction at a distance 0.5 m on the axial line of a bar - magnet of length 5 cm and polestrength (June 2008) 16. What are Ferromagnetic Substances? (March 2009)

8.1 THEORY OF MAGNESTISM Short Answer Questions 1. Distinguish between magnetic and nonmagnetic substances. (T.Q.)

2. Explain why isolated magnetic poles do not exist. (T.Q.) A. If a bar magnet is cut into smaller and smaller pieces till we get the smallest possible piece, we find that the smallest - piece will behave as a magnet with its own N - pole and S - pole. Hence we learn that poles of a magnet exist together as a pair. They cannot be separated.

Very Short Answer Questions 1. What is the reason for the magnetism exhibited by magnetic substances? A. The reason for the exhibition of magnetism by magnetic substances is the configuration of electrons in atoms or groups of atoms in those substances.

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2. Why is steel used to make permanent magnets? A. In steel the alignment of molecular magnets produced during the magnetisation remains permanent. Therefore steel is used to make permanent magnets. 3. Why is soft iron used to make electromagnet? A. In soft iron the alignment of molecular magnets is disturbed easily. So soft iron is used to make electromagnet. 4. What are the magnetic substances? A. Substances which are affected by a magnet are called magnate substances. 5. What is the main property of a magnet? A. Directive property (Showing north and south of earth when freely suspended). 6. Iron filings in a test tube do not behave like magnets why? A. Because Iron filings are randomly arranged.

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Long Answer Questions 1. What are the essential ideas of Ewingâ&#x20AC;&#x2122;s molecular theory of magnetism? (T.Q.) (March 2002) A. Molecular theory of magnetism was firstly proposed by Weber in 1852 and later it was developed by Ewing in the year 1890. Its main features are: 1) Every molecule of a magnetic substance behaves â&#x20AC;&#x2DC;as a tiny magnet called molecular magnet. When a magnet is made into a number of pieces, each piece acts as an individual magnet with north and south poles. 2) Like poles repel each other and unlike poles attract each other. A magnet will have maximum strength at the poles and the two poles of a magnet will have equal strength. 3) In an unmagnetised state the molecular magnets in an Iron bar are randomly distributed with the north and south poles pointing in all possible directions which results in the net magnetic effect equal to zero. 4) When an Iron bar is magnetised, the molecular magnets are arranged in an order such that all the north poles point in one direction and all the south poles point in the opposite direction. 5) On magnetizing an Iron bar, its length will be found slightly greater due to the arrangement of molecules in proper order. 6) In certain substances like steel, the alignment of molecular magnets produced during the magnetisation remains permanent, therefore it is used to make permanent magnets. But in some substances like Iron, the alignment is disturbed easily. Hence it is used to make electromagnets.

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Drawbacks (failures) Ewings molecular theory failed to explain why 1) The individual molecules of magnetic substance like iron behave as tiny magnets. 2) The individual molecules of non-magnetic substance like brass or paper etc., not as tiny magnets. 3) The substances like bismuth, copper etc., are repelled by a strong magnet.

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8.2 INVERESE SQUARE LAW OF MAGNETISM Short Answer Questions 1. Distinguish between absolute and relative permeability of a medium. (T.Q.)

2. State and explain Inverse square law of Magnetism. (March 2012, 2010, 2009) A. 1) Inverse square law: The force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths (rn1 m2) and inversely proportional to the square of the distance (r2) between them. 2) In S.I. system, in any other media the inverse square law can be written as Here t is called absolute permeability of media. 3. Mention the units of magnetic flux density. A. The units of magnetic flux density are 1) Weber /m2 or Tesla. 2) Newton / ampere â&#x20AC;&#x201D; metre i.e., N/A - m.

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Very Short Answer Questions 1. Define the term pole strength of a bar magnet. (T.Q.) A. The ability of a pole of a magnet to attract or repel another magnetic pole is called its pole strength. 2. State the inverse square law of magnetism. (T.Q.) (March 2004, June 2000) A. The inverse square law of magnetism states that, the force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them and acts along the line joining the poles. 3. What is magnetic unit pole strength? (T.Q.) A. The unit magnetic pole is defined as that pole which repels an identical pole at 1 metre distance with a force of 4. Define magnetic flux density. (March 2011) (T.Q.) A. The magnetic flux passing through a unit normal area is called magnetic flux density.

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5. Define magnetic flux. A. The total number of magnetic lines of force in a given area is called magnetic flux (). 6. What is the unit of magnetic flux? A. Magnetic flux is measured in Weber. 7. What is the relation between Tesla and Gauss?

8. What is Gauss? A. Gauss is a C.G.S unit of intensity of magnetic field.

9. Define intensity of magnetic field. A. The intensity of magnetic field (H) at a point is defined as the force acting on a unit north pole placed at that point, independent of the medium. 10. What is the C.G.S. unit of intensity of magnetic field? A. Gauss. 11. What is relative permeability? A. Relative permeability : It is the ratio of absolute permeability of the medium to the permeability of free space. It has no units.(Or) The ratio of the magnetic force in a medium to the magnetic force in free space. 12. Define magnetic field?

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A. The space around the magnet in which its influence is felt is called magnetic field. 13. Give the units of pole strength? A. Units of pole strength: In MKS system Weber In S.I system: Ampere-meter. 14. Is coulombâ&#x20AC;&#x2122;s inverse square law real? A. No. It is hypothetical as isolated poles do not exist.

16. What is the relation between Weber and Ampere-meter?

17. Give the units of relative permeability A.

has no units since it is a mere ratio of two similar

18. What is value of A.

for air or vacuum?

= 1 for air or vacuum.

19. Give the units of magnetic flux density. A.

or Tesla (1).

20. Give the relation between B and H. A.

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Long Answer Questions 1.State and explain inverse square law of magnetism A. Inverse square law: The force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths (ml m2) and inversely proportional to the square of the distance (r2) between them. Derivation: 1) Let the two poles of strengths m1 and rn2 are separated by the distance of ‘r and force between them is ‘F’. 2) The force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths. 3) The force of attraction or repulsion between two magnetic poles is inversely proportional to square of the distance between them.

From equations (1) and (2), we have Here k is a proportionality constant which depends on the media. 4) In S.I. system in free space the inverse square law of magnetism can be written as Here is called magnetic permeability of free space. 5) In S.I. system, in any other media the inverse square law can be written as

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Here is called absolute permeability of media.

8.3 MAGNETIC FIELD DUE TO A BAR MAGNET Short Answer Question 1. What are the values of magnetic induction at a distance don axial line and on an equatorial line of a bar magnet? (March 2007) (T.Q.)

Very Short Answer Questions 1. What is meant by magnetic moment? What are its units in S.I. system? (June â&#x20AC;&#x2DC;05, â&#x20AC;&#x2DC;00) A. The product of pole strength and magnetic length is called magnetic moment. Magnetic moment (M)

2. What is the S.I. unit of magnetic moment? A. The S.I. unit of magnetic moment is

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3. Define the axial line of a magnet. A. The imaginary line joining the north and south poles and passing through the centre of mass of a magnet is called the axial line. 4. Define equatorial line of a magnet. A. The imaginary line passing through the centre of mass and perpendicular to the line joining the poles of a bar magnet is called equatorial line.

Long Answer Questions 1. What is magnetic moment of a bar magnet? How do you measure it? (T.Q.) (March ‘13) A. 1) When a bar-magnet of pole strength m and length 2l is suspended freely in air, it always turns along the magnetic north (N) arid south (S) poles of the earth. 2) This is because the bar - magnet is acted upon by a ‘couple’ constituted by two parallel forces separated by a distance 2l equal to the length of the magnet. 3) In terms of this couple, an important property called ‘magnetic moment’ denoted by M is defined for the bar-magnet. 4) Magnetic moment (M) of a bar-magnet is measured by the product of its pole strength (m).and its magnetic length (2l). i.e., magnetic moment, M = 2l m 5) The S.I. units of magnetic moment are ampere-

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2. What is the value of magnetic induction at a distance d on the axial line of a bar magnet? Explain. (March 2007)

Magnetic Field Induction on the Axial Line: 1) NS is the bar magnet of length 2l and pole strength m, so that’ its magnetic moment M =m x 2l 2) ‘F’ is a point at a distance ‘d’ on the axial line of the magnet. 3) The resultant force due to the magnetic poles of the magnet on a unit N-pole plated at ‘F, is the magnetic induction ‘B’.

3. What is the value of magnetic induction at a distance ‘d’ on the equatorial line of a bar magnet? Explain. (March 2003) A. Magnetic Field Induction on the Equatorial Line: 1) NS is a bar magnet of length 2l and pole strength m so that its magnetic moment M = m x 21. 2) F is a point at a distanced’ from the centre of the magnet on its equatorial line.

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3) The resultant force due to the magnetic poles of the magnet on a unit N-pole placed at F is the magnetic induction.

8.4 MAPPING OF MAGNETIC LINES OF FORCE DUE TO A BAR MAGNET: NEUTRAL POINTS Very Short Answer Questions 1. What are the neutral points of a bar magnet? (T.Q.) A. A point where the magnetic field induction (B) due to a bar magnet is equal in magnitude and opposite in direction to the horizontal component of earths magnetic field induction (Bo) is called a neutral point. 2. How can the neutral points of a bar - magnet be located? A. The neutral points of a bar-magnet can be located by mapping magnetic lines of force using a compass. 3. Where do the neutral points lie when the north pole of a bar magnet points towards geographical north? A. When N - pole of a bar magnet points towards the geographical north, the two neutral points lie on the equatorial line of the bar-magnet such that they are equidistant from the centre of the magnet.

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4. What is the value of B0 in Andhra Pradesh? A. 5. When the N-pole of the magnet is placed facing the N-pole of earth, where will the neutral points be found? A. On the equatorial line. 6. Give the formula to find magnetic moment of a bar-magnet when neutral points are on the axial line.

Long Answer Questions 1. How do you locate the neutral points when the north pole of a bar - magnet faces geographical north and when the south pole of a bar-magnet faces geographical north? (T.Q.) A. Location of neutral points when the north pole of a bar-magnetic faces geographical north: 1) Fix a drawing sheet on a drawing board. 2) Take a compass needle and identify the magnetic meridian i.e., the direction of N and S poles of the earth. 3) Take a bar - magnet and place it at the centre of the sheet such that its N-pole points towards the N-pole of the earth. 4) Now place the compass at different points on the right side of the bar magnet NS and starting at N-pole, mark the points corresponding to N and S poles of the compass needle Thus, draw the magnetic lines of force by the procedure.

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5) At a point N1 on the right side at a distance d from the centre 0 of the magnet, we observe that the magnetic needle in the compass does not show any specific direction. This is one neutral point. 6) Similar behaviour will be observed on left side at N2. This is second neutral point. In this position, the two neutral points lie on the equatorial line of the bar-magnet. Location of neutral points when south pole faces north pole of the earth: 1) In this case, let the S-pole of the bar- magnet point towards N-pole of the earth. 2) Repeat the procedure for mapping the magnetic lines of force using the compass 3) At a point N1 on the top of the S pole of the bar - magnet, the compass will not show any specific direction This is one neutral point 4) Similarly at a point N2 below the N-pole of the magnet is another 5) In this position these neutral points lie on the axial line of the bar-magnet. 2. How do you calculate the magnetic moment and pole strength of a bar magnet from the knowledge of neutral points of a bar magnet? (T.Q.) A. Since at a neutral point, the magnetic field due to a bar - magnet B is equal and opposite to the horizontal component of earthâ&#x20AC;&#x2122;s magnetic field induction (Bo), we can calculate magnetic moment (M) and hence pole strength (m) of the bar - magnet, provided we have the knowledge of B0 at the place. For example, the value of B0 in Andhra Pradesh State is about

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Case (I): When the neutral points are on the equatorial line of a barmagnet at a distance d from the centre of the magnet, we have

Knowing the value of d from the experiment, M can be calculated. If 21 is the length of the bar magnet, the pole strength (m) can be calculated from

Case ii) : When then neutral points are on the axial line of a bar - magnet at a distance ciâ&#x20AC;&#x2122; from its centre, we have

At the neutral point, Since d value is known from the experiment, M can be calculated. Hence the pole strength,

where 2l is the length of the bar-magnet.

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PROBLEMS 1. Calculate the value of the magnetic induction at a distance 0.5 m on the axial line of a bar - magnet of length 5 cm and pole strength 2 x 10-3 A-m. (June 2008) (T.Q.) Sol. 1) Given: 2l=5cm=0.05m; m=2x10- 3A-m;d=0.5m; B? We know

= 10-7 Henry/metre.

2) Formula 3) 2. Calculate the magnetic induction at a distance 0.5 m from the centre of a short bar - magnet on the equatorial line of a bar â&#x20AC;&#x201C; magnet of length 5 cm and pole strength 2 x 10 -3 ampere metre. (T.Q.) (April â&#x20AC;&#x2DC;08, March 2005) Sol. 1) Given: 2l=5cm=0.05m; m=2x10 -3A-m d=0.5m,

= 10 Henry/meter, B=?, M =mx2I =2 x10 x0.05 =1 x10Amp-meter 2

2) Formula:

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3. The north pole of a short magnet of length 5 cm is facing the geographical north. The pole strength of the magnet is 3 x 10 -2 ampere-meter. Find the position of the neutral points.(T.Q.) Sol. 1) Given : 2l = 5 cm = 0.05 m; m = 3 x 10 -2 amp - met. M=mx2l=3x10 -2x0.05 1.5x10 -3A-m2. 2) Formula: M= 390 d 3 (equatorial line) ord = 1.567 x 10 -2 m =1.567cm 4. Calculate the magnetic moment of a short bar magnet of length 5 cm and pole strength 2x10 -3A-m Sol. Given2l=5cm=0.05m m = 2 x 10 -3 A-m Magnetic moment M =? M=2lxm=0.05x2x10 -3=0.1x10 -4=101A-m2 5. Find the value of the magnetic moment and pole strength of a short magnet when the neutral points are on its equatorial line at a distance â&#x20AC;&#x2DC;dâ&#x20AC;&#x2122;. (Given B = B0 = 0.39 x 10 -4Tesla). Sol. 1) Given: B = B0 = 0.39 x 10 Tesla. We know 2) Formula: 3) M = 0.39 x 10 -4=

x d3 = 390d3

4) But M = m x 2l (or) Pole strength m= 5)

=10 -7Henry/metre

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6. Find the value of the magnetic moment and pole strength of short magnet when the neutral points are on its axial line at a distance â&#x20AC;&#x2DC;dâ&#x20AC;&#x2122; (Given B = B0 = 0.39 x 10 -4TesIa) Sol. 1) Given: B= B0= 0.39 x 10 -4Tesla and we know Henry/metre 2) Formula: 3) 4) But m x 2l= (or) Pole strength m= 2l is the length of the magnet.

=10 -7

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Diagrams 1.Draw a neat labelled diagram showing magnetic lines of force, when the south pole of bar-magnet faces geographical north and locate the neutral points. (June ‘02, ‘01, Oct. ‘99)

2. Draw the figure showing the magnetic lines of force and neutral points when the N - pole of a bar magnet faces N - pole of the earth. (June 2005, March 2003)

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8.5 MAGNETIC PROPERTIES OF MATERIALS Short Answer Questions 1. What are diamagnetic substances? Give some examples. (T.Q.) A. Diamagnetic substances are those in which the resultant magnetic moment of individual atoms is zero. Eg: Gold, Alcohol, Mercury, Hydrogen, Air, Water, Bismuth, Copper etc. 2. What are paramagnetic substances? Give examples. (T.Q.) A. Paramagnetic substances are those in which the resultant magnetic moment of the individual atoms is not zero. Eg: Aluminium, Platinum, Chromium, Oxygen, Solutions of salts of nickel and Manganese. 3. What are ferromagnetic substances? Give some examples. (March 2009, June 2003) (T.Q.) A. Ferromagnetic substances are those in which the resistant magnetic moments of individual atoms align themselves in parallel because of a special effect present in them giving rise to spontaneous magnetisation. Eg: Iron, Cobalt, Nickel, Gadolinium and Dysprosium etc. 4. Compare the values of relative permeability and magnetic susceptibility of dia, para and ferromagnetic substances. (June ‘07, ‘06, ‘04, March ‘04, ‘01)

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5. What is spontaneous magnetisation? In which material do you observe it? (T.Q.) A. 1) Spontaneous magnetisation is the magnetisation which causes due to the special effect called exchange coupling between the adjacent atoms in the solids. 2) Spontaneous magnetisation is observed in ferromagnetic substances. 6. Define the terms. a) Magnetic susceptibility b) Magnetic permeability. (March 2002) A. (a) Magnetic susceptibility: The ratio of intensity of the magnetisation (1) to the intensity of applied magnetic field (H) is called magnetic susceptibility (b) Magnetic permeability: The ability of the medium to allow the magnetic lines of force to pass through it is called magnetic permeability. 7. What is â&#x20AC;&#x2DC;exchange couplingâ&#x20AC;&#x2122;? A. In ferromagnetic substances like iron, there is always some amount of intensity of magnetisation even though the applied magnetic field is zero. This inherent or spontaneous magnetisation is due to the special effect called exchange couplingâ&#x20AC;&#x2122; between adjacent atoms in the solid.

Very Short Answer Questions 1. What are domains in a ferromagnetic specimen? (T.Q.) A. Domain in a ferromagnetic specimen is a small local region in which all the magnetic dipoles align parallel to each other giving rise to certain magnetisation with in the domain.

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2. Define intensity of magnetisation. (March- 2011) A. The magnetic moment acquired by a substance per unit volume is defined as the intensity of magnetisation (I). 3. What are the units of magnetic susceptibility? A. Magnetic susceptibility has no units. 4. What is meant by Retentivity of a magnetic material? A. Retentivity of a magnetic material is a property by virtue of which it retains certain amount of intensity of magnetisation even after the removal of applied magnetic field. 5. Define magnetisation? A. The ability of a material to get magnetised when placed in an external magnetic field is called magnetisation. 6. Write the units of intensity of magnetisation.

7. Define magnetic susceptibility. A. It is the ratio of intensity of the magnetisation (I) and the intensity of applied magnetic field

8. Give an example of a substance with maximum susceptibility. A. Soft iron.

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9. Give an example of a substance with maximum retentivity? A. Steel. 10. Give the relation among x I and H. A.

(dimension less) where I: Intensity of magnetisation H : Intensity of applied magnetic field : Susceptibility

11. What is the value of relative permeability substance? A.

for diamagnetic substance is less than or equal to 1.

12. What is the value of relative permeability substance? A.

of diamagnetic

of paramagnetic

for paramagnetic substance is slightly greater than 1.

Long Answer Questions 1. Why a ferromagnetic substance like iron rod is not a magnet by itself? Explain on the basis of domain theory. (Mar 08)(T.Q.) (Imp.) A.1)In a ferromagnetic substance, large number of domains occur 2) The direction of magnetisation within a domain is different from that in the neighbouring domains as shown in figure

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3) Here boundary lines indicate the domains and the arrow shows total magnetisation 4) We observe from the figure that the arrows within the domains point along different direction 5) As a result the net magnetisation of the specimen as a whole is almost zero. This is why an iron rod is not a magnet by itself. 6) However, when iron rod is magnetised, the domains expand in space such that all the arrows align parallel to each other in a single direction. Thus the specimen acquires N and S poles and become magnet. 2. Distinguish between Dia, Para, Ferromagnetic substances. (Or) Explain the Dia, Para, Ferro magnetic substances. (June â&#x20AC;&#x2DC;00, March â&#x20AC;&#x2DC;99) A. Distinguish between Dia, Para, Ferro magnetic substances:

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UNIT-9 A. CURRENT ELECTRICITY

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INTRODUCTION Electricity is defined as the study of flow of electric current and its properties. Electricity commonly occurs due to many facts such as electric charge, electric current, electro magnets, and electric power. An electric charge is negatively charged particles produced by the some well known process. These negative particles are called electrons in science terminology when these electrons move freely through a medium then electric current is produced. Electricity is human made as well as naturally produced. In natural you would have observed a thunder bolt lighting fastly it is a naturally electric current produced by clouds before rain, like wise many chemicals also produce electricity such as mercury, lithium etcâ&#x20AC;Ś Artificially water is run through a rotating turbine to produce electricity which is also called as hydro electricity. Likewise thermal and solar energy is also used for electricity. Scientist has found that we can make electricity if we pass a magnet close to metal wise. Electric charge is both positive and negative. Where two like charges repel each other. Metals are good conductors of electricity about which we have studied an experiment in the previous lessons. The one which allows the current to pass through them are called as semi conductors. Likewise in nature there are many conductors, many insulators and many semiconductors in this world. In this chapter we are going to discuss the various type of conventions and type of materials used in electricity like mostly semiconductors.

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HISTORY Long before any knowledge of electricity existed people were aware of shocks from electric fish. Ancient Egyptians texts dating from 2750BC referred as thunder of Nile. The first discoveries of electricity were made back in ancient Greece. Greek Philosopher discovered that when Amber is rubbed against cloth, lightweight object will stick to it, this is the basis of static electricity. Over the centuries , there have been many discoveries made about electricity we have all heard of famous people like Benjamin Franklin and Thomas Edison, but there have many other inventors throughout history, that were each a part in the development of electricity. The credit for generating electric current on a practical scales goes to famous English scientist Michael Faraday who was greater interested in the invention of the electromagnetic but his brilliant mind took earlier experiment still further . He thought of a question that if electricity could produce magnetism, why magnetism couldn’t produce electricity. In 1831 Faraday found the solution that electricity could be produced through magnetism by motion he discovered the first method of generating electricity by means of motion in a magnetic field. Edison used his DC generator to provide electricity to light his laboratory and later to illuminate the first New York street to be lit by electric camps in September 1882. He was success at least after failure for 200 times. Likewise there are many inventions of electricity by the following great personalities      

Thomas Alva Edison Galvani and Volta Michael Faraday Joseph Swan Nikida Tesla James Watt

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 Andre ampere  George ohms

 SCIENTIST BIOGRAPHY

Michael Faraday, FRS (22 September 1791 – 25 August 1867) was an English scientist who contributed to the fields of electromagnetism and electrochemistry. His main discoveries include those of electromagnetic induction, diamagnetism and electrolysis. It was by his research on the magnetic field around a conductor carrying a direct current that Faraday established the basis for the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light and that there was an underlying relationship between the two phenomena. Faraday was born in Newington Butts,[7] which is now part of the London Borough of Southward, but which was then a suburban part of Surrey.[8] His family was not well off; his father, James, was a member of the Glassine sect of Christianity. James Faraday moved his wife and two children to London during the winter of 1790 from out gill in Westmorland, where he had been an apprentice to the village blacksmith. At fourteen he became the apprentice to George Reba, a local bookbinder and bookseller in Bland ford Street.[11] During his seven-year apprenticeship he read many books, including Isaac Watts' The Improvement of the Mind, and he enthusiastically implemented the principles and suggestions contained therein. At this time he also developed an interest in science, especially in electricity. Faraday was particularly inspired by the book Conversations on Chemistry by Jane Marcet

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Faraday married Sarah Barnard (1800–1879) on 12 June 1821. [14] They met through their families at the Sandemanian church, and he confessed his faith to the Sandemanian congregation the month after they were married. They had no children .Faraday is best known for his work regarding electricity and magnetism. His first recorded experiment was the construction of a voltaic pile with seven halfpence pieces, stacked together with seven disks of sheet zinc, and six pieces of paper moistened with salt water. With this pile he decomposed sulphate of magnesia. In 1821, soon after the Danish physicist and chemist Hans Christian Orsted discovered the phenomenon of electromagnetism, Davy and British scientist William Hyde Wollaston tried, but failed, to design an electric motor.[3] Faraday, having discussed the problem with the two men, went on to build two devices to produce what he called "electromagnetic rotation”. Faraday’s breakthrough came when he wrapped two insulated coils of wire around an iron ring, and found that, upon passing a current through one coil, a momentary current was induced in the other coil. [3] This phenomenon is now known as mutual induction. Faraday died at his house at Hampton Court on 25 August 1867 aged 75 years and 11 months.[21] He had previously turned down burial in Westminster Abbey, but he has a memorial plaque there, near Isaac Newton's tomb

USES FO ELECTRICITY From the invention of electricity current till the date, there was utmost use of electricity, the use of electricity everywhere in this world. we cannot explain where and how was electricity is used because it is a wide range of application used in the world wide but the type of production of electricity can be explained There are three types where electricity can be produced as follows

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HYDEL ELECTRICITY: Water is allowed to run on the turbines to produce the electric charge, it is mostly used in places where water sources are high THERMAL ELECTRCITY: Thermal electricity is the process of conversion of heat energy to electric energy mostly coal is used as a source to develop thermal energy

SOLAR ELECTRCITY: It is a method of absorption of heat energy from the sun and converts into electrical energy. The prominent source is the sun for solar energy WINDMILL: windmill is also used now day to generate electricity. But it is only used in the highly hilly areas.

ELECTRICTY USE IN DAILY LIFE  Generally use in the home appliance such as TV fan mixer grinder etc  Now a day’s electricity is everywhere for example if we take the induction cook top or the rice cooker people are mostly adoptee to it because it save time and there wouldn’t be any observation or care required while cooking

ELECTRICTY BASIC CONCEPTS CURRENT ELECTRICITY: the study of various effects of electrical charges in motion is called as current electricity CURRENT: the net charge flowing through a cross section of a conductor in unit time is called current AMPERE: it is defined as amount of current in ac conductor when the net flow of charge per second through its cross section in one coulomb

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ELECTRICAL POTENTIAL or VOLTAGE: it is work done by moving a unit positive charge from the infinity without any acceleration from the infinity to that point Electric field: it I potential difference between two points said to be one volt, when one joule of work is done in carrying in one coulomb of positive charge from one point to the another against the electric field EMF or Electro motive force: it is defined as the amount of work done by the cell on charge carries to the force them to go to the point of higher potential A simple electric circuit is an arrangement consisting of a source of electrical energy a device which utilizes this energy and conducting wires which connect them CELLS IN SERIES: When a negative terminal of cell is connected to the positive terminal of the next cell then the cell are said to be in series For example : if suppose there are four batteries then the negative terminal of the first battery is connected to the positive terminal of the second battery as so on and at last the terminal ends are connected to the bulb Observation: if we have connected 2 volts batteries of each then the output will be 8 volts the output will be maximum CELLS IN PARLLEL: When all the positive terminal are connected commonly to single point and similarly all the negative terminals are connected to another single point , then cells are said to be parallel For example : if suppose there are three batteries then all the negative terminals are connected to on single point and similarly all the positive terminals are done in the same way as positive is done and connected to bulb

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Observation: if we have connected three batteries of 2volts then the output will be 3 volts only LAW OF RESISTANCE: the law of resistance was discovered by George Simon Ohms hence it was named after ohms law. It states that the resistance of a given circuit is Directly proportional to the voltage  RαV Inversely proportional to the current flowing in the circuit  R α 1/i Therefore resistance of a circuit is defined as  R = V/i ELECTROLYSIS: The process of decomposition of chemical compound in a solution when electric current passes through it is called electrolysis

FARADAYS LAW OF ELECTROLYSIS: In 1833, Michael faraday conducted a series of experiments on liquid electrolyte and two laws of electrolysis which states as below Faradays first law of electrolysis “ The faradays first law of electrolysis states that mass (m) of the ions liberated from an electrolyte is directly proportional to the strength of the current (i) and the time (t) for which the current passes

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 Mαi  Mαt  M α it  m = Zit Where Z is the electro chemical equivalent  Z=m/it

Faradays second law of electrolysis The ratio of atomic weight (A) of an element to its valence (V) is defined as chemical equivalent or equivalent weight “Faradays second law of electrolysis states that same quantity of electricity passes through different electrolytes, the masses of ions liberated at the respective electrodes are proportional to their chemical equivalent m 1 = m 2 = m3 E1 = E 2 = E 3 These are just basic further in the chapter we will come across many topics further which will be in detail.

IMPORTANT POINTS  The study of electric charges at rest is called ‘static electricity’.  The study of various effects of electrical charges in motion is called ‘current electricity’.  The net charge flowing through a cross-section of a conductor in unit time is called   The unit of current is ampere.  Ampere is an amount of current in a conductor, when the net flow of charge per second through its cross-section is one coulomb.

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 Electric potential at a point in space is defined as the work done in moving a single unit positive charge from infinity to that point  The electric potential is measured in units of ‘volts’.  The electric potential difference between two points is said to be one volt, when one joule of work is done in carrying one coulomb of positive charge from one point to another.  A simple electric circuit is an arrangement consisting of a source of electrical energy, a device which utilizes this energy, and conducting wires which connect them.  The symbol of a cell is  When negative terminal of a cell is connected to the positive terminal of the next cell, then the cells are said to be in “series”.  The e.m.f. of three cells connected in series be E1, E2 and E3 then the total e.m.f. in the circuit, E = E1 + E2 + E3.  The electric property of a conductor which opposes the flow of electrons through it is called electric resistance.  Ohm’s law: At constant temperature, the potential difference (V) across a conductor is  The unit of resistance is Ohm and is denoted by the symbol

 Resistance of a conductor ohms where p is the specific resistance.  The specific resistance of a material is defined as the resistance of its specimen of unit length and unit area of cross-section.  The units of specific resistance are ohm-metre.

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 In a circuit, resistors connected end-to-end are said to be in series, if the same current exists in all of them through a single path.  . ‘When resistors are connected in series: the same current passes through all of them.   same p.d. exists across all of them   the reciprocal of the equivalent resistance of the combination is equal to the sum of the reciprocals of the individual resistances.   the equivalent resistance of the combination is less than that of any individual resistance.  When electric current passes through a resistance, heat is produced.  Electrical energy or Electrical work done W = Vq, where V is voltage and q is electric charge.  where i = current, R = resistance and t = time.

 Electric Power, where, V = voltage, i =current and R = resistance.  Wattage of an electrical appliance is defined as the rate at which electrical energy is consumed.  Joule’s Law: A given amount of work done in different ways produces the same quantity of heat in all cases and is directly proportional to heat produced  W = JQ, where J = mechanical equivalent of heat or Joule’s constant.

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 The work required to be done to produce a quantity of heat of 1 calorie is 4.18 Joules.  When current passes through an element, the heat developed .  Watt-Hour is defined as the electrical energy consumed by an appliance of a wattage of 1 watt in an hour.

PREVIOUS EXAMINATION QUESTIONS 1. An electric installation consists of 100 lamps each drawing 0.2 amp at 220V supply. Find the cost of working of installation for a month of 30 days at 5 hours per day, if the energy used is charged at the rate of Rs. 2/- per unit. (March 2007, June 2005) 2. Show that effective resistance of a series of combination in a circuit is equal to the sum of the individual resistances. (or) Derive (June 2006, March 2006, 2004) 3. Calculate the equivalent resistance of two resistors 100 connected in parallel. (June ‘02)

. and 1

4. Define Joule’s law and derive Q = (March 2008, June 2002) 5. Derive an expression for equivalent resistance of parallel combination of three resistances R1, R2 and R3. (April 2008, June 2007, March 2002) 6. The resistance of Manganin wire of 1 cross-sectional area is 15 . find the resistance of the manganin wire of same length but of crosssection of 3 . (June 2001) 7. What are the ohmic and non-ohmic conductors? Give examples of the potential difference across a bulb is 240 V when a current of 3A flows through it. Find the resistance of the bulb. (June 2003, 2001)

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8. What is the total e.m.f. when three cells of voltages 1V, 1.5 V and 2 V are connected in series? (March â&#x20AC;&#x2DC;01) 9. State ohms law: Describe an experiment to verify ohms law. (Mar 05, 01) 10. Draw an electric circuit and label the parts. (March 1999 11. A house is fitted with 10 lamps of each 60 watt. If each lamp burns 5 hours a day, find the cost of consumption in a month of 30 days at the rate of Rs. 2.40 per unit. (June 2004) 12. State the laws of resistance. (March 2007)

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9.1 SIMPLE ELECTRIC CIRCUITS Short Answer Questions I. Write differences between conventional and electronic current.

2. Distinguish between static electricity and current electricity.(T.Q.)

3. Name some power sources and power consumers. (T.Q.) A. Power Sources: Cell, Battery etc.Power Consumers: Tubelight, fan, electric bulb etc. 4. Why are bulbs connected in parallel in the house-hold wiring? A. The bulbs that are connected to the main supply in the houses are all connected in a parallel circuits. This makes it possible to sustain any bulb on or off we like. If a bulb in a room is put off, the bulbs in the other rooms continue to glow.

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5. When bulbs are connected in series, if one of them falls to work, what will happen to other bulbs? Why? A. If one bulb fails to glow other bulbs will not glow, this is due to the break in the circuit.

Very Short Answer Questions 1. Define electric current. (T.Q.) A. The net charge flowing through a cross - section of a conductor in unit time is called current. 2. Define ampere. (T.Q.) A. If one coulomb of charge passes through a cross-section of a conductor in a second, then the current in the conductor is said to be one ampere. 3. Define electric potential at a point. (T.Q.) A. Electric potential at a point is defined as the work done in moving a single positive charge from infinity to that point. 4. What do you mean by potential difference? (T.Q.) A. The amount of work done in carrying unit positive charge from one point to another is called potential difference between the two points. 5. Define volt. (T.Q.) A. If one joule of work is done in carrying one coulomb positive charge from one point to the other, then the potential difference between them is said to be 1 volt.

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6. What is e.m.f. of a cell? (T.Q.) A. The electromotive force (e.m.f.) is defined as the amount of work done by the seat (cell) on the charge carriers to force them to go to the point of higher potential. 7. What is a simple circuit? (T.Q.) A. A simple electric circuit is an arrangement consisting of a source of electrical energy, a device which utilizes this energy and conducting wires which connect them. 8. What is the use of tap key? A. Tap key is used to make and break an electric circuit. 9. What is meant by power source? A. The source which supplies electrical energy is called power source. 10. What is meant by power consumer? A. The device which utilizes the electrical energy is called power consumer. 11. What are called connectors? A. For the consumption of electrical energy, the power source has to be connected to the power consumer with the help of copper wires. Therefore such copper wires or any other conducting wires are called connectors. 12. What is meant by parallel combination of electric bulbs? A. In an electric circuit, bulbs are said to be connected in parallel, if the first terminals of all the bulbs are connected to a common point and similarly all the second terminals to another common point.

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13. When a number of bulbs are connected in series in a circuit, if one of them is removed or fail to work, the rest of the bulbs will not glow. Why? A. When a number of bulbs are connected in series in a circuit, if one of them is removed or if it fails to work, the rest of the bulbs will not glow. This is because removal of the bulb or its failure causes a break in the circuit. 14. When a number of bulbs are connected in parallel in a circuit, if one of them is removed or it fails to work, the rest of the bulbs will continue to glow. Why? A. When a number of bulbs are connected in parallel in a circuit, if one of them is removed or if it fails to work, the rest of the bulbs will continue to glow. This is because, only this particular part of the circuit breaks and all other parts of the circuit remain unaffected even after removal of the bulb or failure of the bulb. 15. Give the symbol for dry cell. A. 16. Give the symbol for battery. A. 17. In which combination current is constant? A. Series combination. 18. In which combination potential difference is constant? A. Parallel combination.

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Long Answer Questions 1. What is the use of tap key? Explain its working. (T.Q.) A. 1) A tap key is used in an electric circuit to pass the current through the circuit or stop the passage of current when it is not required. 2) Tap key consists of a bent Cu strip with 2 screws. 3) The wires connecting the power source and power consumer are connected to the screws of a tap key. 4) By pressing the metal strip we can turn the current on and off without disconnecting the wires.

2. How do you connect cells in series? What is the total e.m.f. of the combination, when they are connected in series? A. 1) When negative terminal of a cell is connected to the positive terminal of the next cells then the cells are said to be in series 2) In Fig three cells of 1. 5 V e m f each are connected in series. They provide a total P.d. of 4.5 volts in the current. 3) Thus, when cells are connected in series, the total p.d. applied by them will be equal to the sum of the potential differences of individual cells. 4) When cells are connected in series, the total p.d. of the combination is the sum or the p.d.s of individual cells. 5) Let the e.m.f.s of three cells connected in series be E1, E2 and E3. Then the total e.m.f. in the

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3. How do you connect cells in parallel? What is the effective e.m.f. of the combination? (T.Q.) A. 1) When all positive terminals of two or more cells are connected to a single point and similarly all the negative terminals are connected to another single point, then the cells are said to be connected in parallel. 2) In Fig., the potential difference between points F (+ve) and Q (-Ve) will be the same as that of any single cell. If three cells of each 1.5 volts are connected in parallel, they together provide the same p.d. of 1.5 volts only. 3) Thus, when cells of equal e.m.f. are connected in parallel, the effective p.d. remains same as that of any one of the cells. If two or more cells of different e.m.f. are connected in parallel, the effective p.d. will be equal to the p.d. of that cell which has greatest e.m.f.

4) Let three cells of e.m.f. E1, E2 and E3 such that E1 >E2> E3 be connected in parallel. The effective e.m.f. E is given by E = E1. In the case of parallel connection, the cells provide energy to the power consumer (bulb) for a longer duration than that provided by a single power source (cell).

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PROBLEMS 1. What is the total quantity of charge flows in 8 minutes when a current of 2 amperes exists in a conductor? (T.Q) Sol. 1) Given: t=8min=8x6oseconds,i=2 amp Q =? 2) Formula: Q = i.t 3) .. Total charge Q = 2 x 8 x 60 =960 coulombs 2. The total e.m.f. of the series combination of three cells of equal e.m.f. is 4.5 volts. What is the e.m.f. of each cell? (T.Q.) Sol. 1) Given : E= E1 + E1 + E1 = 3E1 = 4.5 volts. 2) Formula: E1 = 3) .. e.m.f. of each cell

volts.

3. A total charge of 90 coulombs flows in a conductor during a lime of 5 minutes. What is the strength of current in the conductor? (T.Q.) Sol. 1) Given :q=90 coulombs, t=5 minutes=5 x60s.,i=? 2) Formula i=

=0.3A

4. What is the total e.m.f. when three cells of voltages 1V, 1.5V and 2V are connected in a) Series and b) Parallel ( T.E.) (March 2001) Sol. 1) Given: E1=1V, E2=1.5V, E3=2V. a) E = 7 (connected in series) b) E =? (Connected in parallel) 2) Formula: a) Series connection E = E1 + E2 + E3 :.E=1+l.5+2=4.5volts. 3) Formula: b) Parallel connection: Effective voltage = E = Voltage of cell with highest e.m.f. ... E=2volts

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Diagrams I Draw an electric circuit and label its parts. (March 1999)

2. Draw the circuit showing the series and parallel connection of batteries.

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9.2 ELECTRICAL RESISTACE- OHM’S LAW AND ITS VERIFICATION Short Answer Questions 1. What are ohmic and non-ohmic conductors? Give examples. (1.9.) (June 2001) A. The conductors which obey Ohm’s law are called ohmic conductors or linear conductors. Eg: All the metallic conductors. The devices or conductors which do not obey Ohm’s law are called non-ohmic conductors or non-linear conductors. Eg: Semi conductors and electrolytes. 2. Why is it necessary to use fuses in a house-hold circuit? A. In a house-hold circuit to avoid excessive overloads in the wires and to eliminate fire hazards, electric fuses are used. 3. Why is fuse wire made of lead which has low melting point? A. If excess current flows in the house-hold circuit, the fuse must melt and prevent the flow of current. This is possible when the fuse is made of materials of low melting point. Lead has low melting point. So fuse wires are made of lead.

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Very Short Answer Questions 1. Define ‘electrical resistance’ of a conductor. (T.Q.) A. The electric property of a conductor which opposes the flow of electrons through it is called electric resistance. 2. Define the term ohm. (T.Q.) A. If a potential difference of 1 volt between two ends of a conductor causes a current of 1 ampere in it, then the resistance of the conductor is said to be one ohm. 3. State Ohm’s law. (March 2005, 2001) (T.Q.) A. Ohm’s law states that at constant temperature, the potential difference across a conductor is directly proportional to current (i) through it. 4. What happens to the conductivity of a conductor when the temperature increases? A. Conductivity decreases with rise in temperature. 5. What is the symbol of Rheostat? 6. What is the use of a Rheostat? A. Rheostat is used to regulate the value of current in a circuit. 7. What is the shape of graph for ohmic conductors? A. A straight line passing through origin. 8. What is the relation between resistance and current? A. Resistance and current are inversely related. 9. What are good conductors of electricity? A. All metals and a nonmetal such as Graphite are good conductors of electricity.

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Long Answer Questions 1. Define Ohm’s Law. Describe an experiment to verify Ohm’s law. (T. Q.) (June ‘12, March ‘05, ‘01) A. Ohm’s law: “At constant temperature, the potential difference (V) across a conductor is directly proportional to the current (i) through it”. Experimental verification: 1) Connect a battery (B), an ammeter (A), a Resistance (R) and a rheostat (Rh) in series as shown in the Fig. 2) 2) Then connect a voltmeter across R. Let R be an unknown resistance and its value should be determined. 3) 3) The current in the circuit can be varied with the help of the rheostat (Rh). Adjust the position of the rheostat such that a maximum current flows in the circuit. Then note the readings in the voltmeter and ammeter.

4) Then changing the position of rheostat gradually, repeat the experiment and take about 6 readings. Note down the values of voltage (V) and current (i) in the voltmeter and the ammeter respectively. Tabulate the results in the table given above.

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5) It will be found that the values in the last column will be constant. It means V\i is constant. So Ohm’s law is verified.

PROBLEMS 1. A 1.5 V battery is connected across a small bull? Calculate the resistance of the filament if the current flowing through it is 0.15A. (T.Q.) Sol. 1) Given: V = 1.5 V, I = 0.15 A, r =? 2) Formula: V = ir (Ohm’s law) (or) r= 3) 2. Calculate the current through a resistance of 30 , across which a p.d. of 4.5 V is applied. (T.Q.) Sot. 1) Given : r = 30 Q, V = 4.5 V, i =? 2) Formula: Ohm’s law : V = ir (or) i= 3) 3. The p.d. across a bulb is 240 V and a current of 3A flows through it. Find the resistance of the bulb. (T.E.) (June 2001) Sol. 1) Given: V = 240 V, I = 3A; r =? 2) Formula: V = ir (Ohm’s law), 3) :. Resistance of the bulb r=

=80 ohms.

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4. An immersion heater of resistance 23 ohms is connected to a mains of 230 V supply. How much current flows through it? (T.Q.) Sol. 1) Given: r = 23 ohms, V = 230 V, i =? 2) Formula: V = ir (Ohm’s law) or i=

Diagrams 1. Draw a rough sketch of the graph indicating Ohm’s law.

Ohmic conductors: The conductors which obey Ohm’s law are called ohmic conductors For such conductors the relation between current and potential difference is linear. Hence they are also called linear conductors. All metallic conductors are ohmic conductors. Thus, Ohm’s law is obeyed only by metallic conductors. 2. Draw the graph for non - ohmic devices.

Parts I-current V- potential difference 0- origin Graph for non-ohmic devices between I and V The graph is not a straight line but curved line

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3. Draw the magic triangle (Ohmâ&#x20AC;&#x2122;s Law).

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9.3 LAW OF RESISTANCE Short Answer Questions 1. On what factors does the resistance of a conductor depend? (T.Q.) A. The resistance of a conductor depends on (1) Nature of the material (2)Length of the conductor 3) Area of cross-section of the conductor 4) Temperature. 2. Distinguish between Resistance and Specific Resistance (Resistivity). (T.Q.)

2. State the laws of resistance. ([T.Q.) (March 2007) A. The laws of resistance are: 1) The resistance of conductor of given material is directly proportional to its length, when temperature and area of cross-section remains constant. 2) The resistance of a conductor of a given material is inversely proportional to the area of the cross section when length and temperature remains constant.

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Very Short Answer Questions 1. Define specific resistance of a conductor. (T.Q.) A. The resistance of a conductor having unit area of cross section and unit length is called specific resistance of a conductor or resistivity (p). 2. What are the units of specific resistance? (T.Q.) A. The units of specific resistance are ohm - meter. 3. Write the expression for ‘R’ and ‘p’ of a substance. (T.Q.)

4. What happens to the resistance of a conductor when the temperature increases? A. As the temperature increases resistance of a conductor increases. 5. What happens to resistance of a conductor if its length increases? A. Resistance also increases.

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Long Answer Questions 1. What is meant by specific resistance? Derive . (June 2000) A. Specific resistance: The resistance of the conductor having unit area of cross-section and unit length is called specific resistance or resistivity. It is denoted by the letter p. Derivation: The resistance of the conductor is directly proportional to length of the conductor. The resistance of the conductor is inversely proportional to area of crosssection: By combining (1) and (2) we have

Here

is a proportionality constant called specific resistance or resistivity.

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PROBLEMS 1. The resistance of a manganin wire is R. What will be its resistance if length is doubled and area of cross section is halved? (T.Q.) Sol. 1) The expression for resistance R = 2) Where p is specific resistance, I is length of wire and A is area of cross section. 3) Let R1 be the new resistance when length is double (2l) and area of cross section is halved 4) Then R1= 2. The resistance of an Aluminium wire of 2m length is 7 ohms. What is the resistance of a wire of 8 metre length of the same material and of the same cross - sectional area? (T.Q.) Sol. 1) Given:R1=7ohms,R2=?, l1=2m,l2=8m 2) Formula: 3) 3. The resistance of a copper wire of 300cm and 1 mm2 crosssectional area is 15 ohms. What is the resistance of another wire whose length and area of cross - section are doubled? (T.Q.) Sol. 1) Given: l1= 300 cm, A1 = 1 m.m2, R2 = 15 ohms L2=600cm,A2=2m.m 2,R2=? 2) Formula: 3)

(or) R2 = = 15 ohms; .. R2 15 ohms

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4. A manganin wire of length 10 in has a diameter 1 mm. Calculate its resistance if specific resistance of manganin is 44 x 10â&#x20AC;&#x201D;s ohm metre. (T.Q.) Sol. 1) Given : l = 10 m, 2r = 1 mm (or) r = 0.5 mm

2) Formula: R= 3)

5. What is the resistance of a pure germanium block of dimensions 50 cm x 2 cm x 1 cm across its length. The resistivity of pure germanium is 0.6 x 10 ohm - meter. (EQ.) Sol. 1) Given:1=50cm=0.5m,A=2x1=2cm2=2x10m2 p= 0.6x 10-s ohm-meter, R=?

=0.015 omhs 6. The resistance of a manganin wire of I m length is5 (1 Find the resistance of a wire of 3 in length of same material having the same area of cross - section. (T.E.) Sol. 1) Given : I1 = 1 m, R1 = 5 , I = 3 m, R2 =?

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2) Formula: 3) As the length of the wire increases, its resistance also increases. 7. The resistance of a manganin wire of 1 mm2 cross-sectional area is 150. Find the resistance of manganin wire of same length but of cross-section of 3 mm2. (T.E.) (June 2001) Sol. 1) Given : R1 = 15 0, A1 = 1 mm2, R2 =?, A2 3 mm 2 2) Formula: 3) ..R2= As the area of cross-section of the wire increases, the resistance decreases. 8. Calculate the resistance of 1 km long copper wire of diameter 2 mm. Given that the resistivity of copper is 1.7 x 10 Ohm-meter. (T.Q.) Sol. 1) Given: l= 1 km = 1000 meter, d = 2 mm, therefore, radius r = 1 mm = 10-3 m; p = 1.7 x 10 ohm â&#x20AC;&#x201C;meter 2) Area of cross-section, A = nr2 = 3.14 x (10 _3) 2 m2 = 3.14 x (106) m 2 3) Resistance, R = p 9. The resistant of a brass wire of length 300 m and area of cross section 3.4 x 10-6 m 2 is 6 ohms. Find the specific resistance of the material of the wire. (T.Q.) Sol. 1) Given, 1= 300 , A = 3.4 x 10 m 2 , R = 6 2) Specific resistance, P=

6.8

9.4 RESISTANCES IN SERIES AND PARALLEL

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Short Answer Questions 1 When do you say that resistances are connected in series? (T.Q.) A. In a circuit resistors connected end - to - end are said to be in series, if the same current exists in all of them through a single path. 2. When do you say that resistances are connected in parallel? (T.Q.) A. In a circuit resistors connected to common terminals are said to be in parallel, if identical p.d. exists across all of them, 3. Resistance of a circuit increases when individual resistors are connected in series but it decreases when the resistors are connected in parallel. Why? A. According to the laws of resistance, the resistance increases with increase in length and decreases with increase in area of cross-section of a conductor. This is because, the series combination of resistances is equivalent to increase in the length of a conductor hence the resistance of the circuit increases. Similarly, a parallel combination of resistances is equivalent to increase in the area of cross-section of a conductor hence the resistance of the combination decreases.

Very Short Answer Questions 1. What is equivalent resistance of 3 resistances R1, R2 and R3 are connected in series? (T.Q.) A. Equivalent resistance, R = R1 + R2 รทR3 2. Find an expression for the equivalent resistance of parallel combination of 3 resistances R1, R2 and R3. (T.Q.)

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3. What is meant by resistor? A. Any conductor used in a circuit to provide resistance is called a resistor (R). 4. What is the symbol for resistor? A. The symbol for resistor is

5. What is the unit of resistance? A. Resistance is measured in Volt/ampere or ‘Ohm’.

Long Answer Questions 1. Show that the effective resistance of series combination in a circuit is equal to the sum of their resistances. (T.Q.) (or) Show that R=R1+R2+R3.(March ‘13, ‘06, ‘04, June ‘06)

1) Let the total current in the above circuit be i and let the resistances of the three conductors be R, R2 and R3 and the potential difference across the two ends of the three conductors be V1, V2 and V3 respectively. 2) Let the effective resistance be ‘R’ and the potential difference between the points A and B is

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2. Show that the recipr6cal of the effective resistance of a parallel combination in a circuit is equal to the sum of their ‘reciprocals. (or) ‘(April 2008) Show that A.1) Let the total current in the above circuit be Ii’. Let the resistances of three conductors be R1, R2. and R3 and the current passing through them be i1, i2 and i3 respectively. 2) Let the’ effective resistance be ‘R’ and the potential difference between the ends A and B is ‘V. All the resistances are connected between the same ends. So the p.d. remains same i.e., ‘V.