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Brief Contents
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Preface
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Measurements 1
Measurements
Remember
Chapter Insights
Remember
Before beginning this chapter, you should be able to:
• know the methods involved in application of science -Aim, observation, measurement, systematization and inference;
Before beginning this chapter, you should be able to:
• define physical quantities and system of units; measurement of some physical quantities; difference between mass and weight
• know the methods involved in application of science -Aim, observation, measurement, systematization and inference;
• define physical quantities and system of units; measurement of some physical quantities; difference between mass and weight
NOTE Example: Fa AB EF ,, , , etc.
Remember section will help them to memories and review the previous learning on a particular topics
• define Density, density of a solid and liqiud, variation in density of liquids and gases with temperatures
Key Ideas
An arrow or a short line is drawn above the quantity to represent a vector.
• define Density, density of a solid and liqiud, variation in density of liquids and gases with temperatures
After completing this chapter you should be able to:
Dynamics 3.7
Key Ideas
• understand the different physical quantities and different systems of units
In print vectors are printed in boldface, e.g., F, a, AB, EF, etc.
After completing this chapter you should be able to:
DISTANCE AND DISPLACEMENT
Thus, we see that moving bodies possess a physical quantity associated with their motion which determines how much force is required to bring them to rest. This quantity which depends on the mass and velocity of the moving body is called ‘momentum’ and is defined as momentum (p) = mass (m) × velocity (v)
Distance
NOTE
• understand the different physical quantities and different systems of units
• recognize the importance of accuracy of measurements and to understand how vernier callipers is used to measure the length more accurately
• study the methods of determining physical quantities like area, volume, mass and density
Distance is defined as the length of the actual path described by a particle in motion. The unit of distance is centimetre in C.G.S. system and metre in M.K.S. or S.I. system.
(i) Since mass is a scalar and velocity is a vector, momentum is a vector quantity.
Displacement
• recognize the importance of accuracy of measurements and to understand how vernier callipers is used to measure the length more accurately
• find the relation between various physical quantities
Text: concepts are explained in a well structured and lucid manner
• study the methods of determining physical quantities like area, volume, mass and density
(ii) If a body is moving along a straight path, the body is said to possess ‘linear momentum’.
Displacement is defined as the shortest distance between the initial and final positions of a body. It is a vector quantity, whose magnitude is equal to the length of the straight line path from the initial position to the final position and the direction is along the straight line drawn from the initial to the final position.
Chapter 2 2.4
• find the relation between various physical quantities
Units of Momentum
Note boxes are some add-on information of related topics
Since p = mv, units of momentum = (unit of mass) × (unit of velocity) = g cm s–1 (in C.G.S system) and kg m s–1 (in SI system) 1 kg m s–1 = 105g cm s–1
The distance travelled by a particle depends on the path traced by the particle, whereas the displacement of a particle in motion is independent of the path traced and depends only on the initial and final positions of the particle.
An arrow or a short line is drawn above the quantity to represent a vector.
Consider a particle moving along the path ABCD as shown below:
EXAMPLE
NOTE Example: Fa AB EF ,, , , etc.
In print vectors are printed in boldface, e.g., F, a, AB, EF, etc.
The speeds of a tortoise and a hare are 2 m s−1 and 5 m s−1, respectively. The mass of the hare is 3 kg and that of the tortoise is 10 kg. Which of the two has greater momentum?
(Assume speed of each to be steady.)
SOLUTION
DISTANCE AND DISPLACEMENT
Distance
2.2
We have seen above that momentum = mass × velocity
Examples given topicwise to apply the concepts learned in a particular chapter
Distance is defined as the length of the actual path described by a particle in motion. The unit of distance is centimetre in C.G.S. system and metre in M.K.S. or S.I. system.
Displacement
The distance travelled by the particle = 6 + 2 + 5 = 13 m. The displacement is the vector AD , whose magnitude is the length of the line segment AD
Velocity being a vector has both magnitude and direction. In the question, only the magnitude of velocity, i.e., speed, is given. There is no information regarding the direction of motion of the hare and the tortoise. Since it is not possible to compare two vectors, it is not possible to compare their momenta. However, we can compare the magnitudes of their momenta as below.
Example: A cop gets information that a thief is 5 km away from the police station. Is it possible for the cop to trace the thief with the given information?
Mass of tortoise = 10 kg.
Speed of tortoise = 2 m s 1
Displacement is defined as the shortest distance between the initial and final positions of a body. It is a vector quantity, whose magnitude is equal to the length of the straight line path from the initial position to the final position and the direction is along the straight line drawn from the initial to the final position.
It is not be possible to trace the thief, as the cop doesn’t know the direction in which to chase the thief. Thus, the information about distance alone is not sufficient to locate the position of a body.
ptortoise = 10 × 2 = 20 kg m s 1
Mass of the hare = 3 kg
Illustrative examples solved in a logical and step-wise manner
The distance travelled by a particle depends on the path traced by the particle, whereas the displacement of a particle in motion is independent of the path traced and depends only on the initial and final positions of the particle.
Consider a particle moving along the path ABCD as shown below:
Dynamics 3.33
TEST YOUR CONCEPTS
Very Short Answer Type Questions
1. State Newton’s first law of motion.
Chapter 3 3.34
16. Define centre of gravity.
40. State and explain the conditions necessary for equilibrium.
2. Mass of a body is a ________ quantity whereas its weight is a ________ quantity.
3. Define inertia.
4. ________ is the measure of inertia.
5. Define momentum.
41. Find the effort required to lift a load of 50 kgwt using a simple machine if its mechanical advantage is
17. A plumb line is used to determine the center of gravity of ________ lamina.
42. Derive the mechanical advantage of single fixed pulley?
6. ________ is the physical quantity that changes or tends to change the state of rest or of uniform motion of a body.
7. The rate of change of momentum of a body is proportional to __________.
8. Define newton.
18. A bottle standing on its base is more stable than when it stands on its neck. This is so because when it stands on the base its __________.
19. State the different types of equilibrium.
Essay Type Questions
43. Why are passengers travelling in a double decker bus allowed to stand in a lower deck, but not in the upper deck?
44. What is the efficiency of a machine, given mechanical advantage is 2 and velocity ratio is 4?
45. Derive the mechanical advantage of single movable pulley?
20. Friction in moving parts of a machine can be reduced by using _____________.
21. Give three examples of bodies in unstable equilibrium.
46. State and prove the law of conservation of momentum.
22. What is a simple machine?
47. Obtain the relation between mechanical advantage, velocity ratio and efficiency.
9. When the mass of a body is kept constant, its acceleration is directly proportional to the ________ acting on it.
23. Bottle lid opener is an example of ______ lever
24. (i) What is mechanical advantage? (ii) Define efficiency of a machine.
48. Explain how the centre of gravity of an annular ring is determined.
10. Powder is sprinkled on a carom board to reduce the ________.
1
12. Define work.
13. What is energy?
Different levels of questions have been included in the Test Your Concept as well as on Concept Application which will help students to develop the problem-solving skill
49. Describe an experiment to determine mechanical advantage of an inclined plane.
50. Explain how the centre of gravity of an irregular lamina is determined.
25. One S.I. unit of force is _______ times one unit of force in CGS system.
CONCEPT APPLICATION
11. A constant force of 2 N acts on a body for 5 seconds to change its velocity. The change in its momentum is _____________.
Level 1
14. 1 newton = ________ dynes.
15. What is a rigid body?
Short Answer Type Questions
31. Derive F = ma
26. What is a lever?
27. See-saw is an example of ________ order lever.
28. What is a first order lever?
Directions for questions 1 to 7:
29. The mechanical advantage of a broomstick is ________.
Fill in the blanks
30. What is the use of a pulley?
State whether the following statements are true or false.
1. All mechanical forces are contact forces.
Match the following
32. Explain the inertia of rest through some examples.
‘Test Your Concepts’ at the end of the chapter for classroom preparations ‘Concept Application’ section with problems divided as per complexity:
2. A constant external force acts on a body in motion. If the mass of the body is doubled with the force remaining the same, its acceleration also doubles.
33. An empty truck of mass 1000 kg is moving at a speed of 36 km h–1. It is loaded with 500 kg material on its way and again moves with the same speed. Will the momentum of the truck remain the same after loading? If not, find the momentum of the truck after loaded.
Level 1; Level 2; and Level 3
QUESTIONS
Directions for questions 8 to 14: Fill in the blanks.
8. Newton’s first law of motion is also called law of ________.
36. Explain how the position of the centre of gravity determines whether a body is in stable or unstable equilibrium.
Multiple choice Questions
3. The principle used in swimming is Newton’s third law of motion.
4. A bottle opener is an example of second order lever.
34. Distinguish between the mass and the weight of a body.
5. Whenever a force is applied on a body, work is done.
35. A railway wagon of mass 1000 kg is pulled with a force of 10000 N. What is its acceleration?
37. Explain the motion of a rocket as an application of Newton’s third law of motion.
Explanation for questions 31 to 45:
6. The line drawn in the direction of force is called the line of action of that force.
QUESTIONS
9. A wheel barrow is an example of ________ order of lever.
10. For greater stability, the position of center of gravity should be low and base area should be _________.
38. A railway engine of mass 2 tons moving at a speed of 72 km h–1 collides with a wagon at rest. After collision both have a common velocity of 36 km h–1 Find the mass of the wagon. (1 ton = 1000 kg)
39. Find the centre of gravity of a triangular lamina, each side of which measures 93 cm
7. Frictional force always acts in a direction opposite to the weight of the body.
11. The force exerted by a body on the earth is ________ the force exerted by the earth on the body.
PRACTICE
12. ‘A’ can finish certain work in one day and B can finish the same work in two days. The ratio of energy spent by A to that spent by B is _____.
31. The force of attraction between an electron and a nucleus is an electrostatic force.
13. Momentum is the product of ____ and ____.
32. Friction in moving parts a machine can be reduced by using lubricants and ball bearings.
37. (1) Action and reaction always act on two different bodies. (2) They are equal in magnitude but opposite in direction.
14. A car changes its speed from 20 km h 1 to 50 km h 1 This is possible only if ______ is applied on the car.
33. When ball is thrown in upward direction, its weight always acts in downward direction and as the body is moving upward, frictional force (due to air) acts in downward direction.
34. Friction can be reduced by (i) using lubricants in machine parts. (ii) polishing surface of bodies in contact.
35. By Newton’s 2nd law of motion, the rate of change of momentum of a body is directly proportional to the force acting on the body.
36. By Newton’s 2nd law
38. Given m = 3 kg
s = 15 m t = 3 s
u = 0
Frictional force, ff = 2 N. (a)
15 03 1 2 32 =× +× × a a = 10 3 m s-2
Hints and Explanation for key questions along with highlights on the common mistakes that students usually make in the examinations
39. Given m1 = 500 g = 1 2 kg , m2 = 250 g = 1 4 kg (b) u1 = 10 m s-1, u2 = –2 m s–1 (d) Momentum before collision, m1 u1 + m2 u2
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Chapter Measurements 1
Remember
Before beginning this chapter, you should be able to:
• Know the methods involved in application of science—aim, observation, measurement, systematization and inference
• Define physical quantities and system of units; measurement of some physical quantities; difference between mass and weight
• Define density, density of a solid and liqiud, variation in density of liquids and gases with temperatures
Key Ideas
After completing this chapter you should be able to:
• Under stand the different physical quantities and different systems of units
• Recognize the importance of accuracy of measurements and to understand how vernier callipers is used to measure the length more accurately
• Study the methods of deter mining physical quantities like area, volume, mass and density
• Find the relation between various physical quantities
INTRODUCTION
Physics deals with nature and its laws. It describes laws of nature quantitatively and qualitatively. This description involves measurement of various physical quantities like height, weight, time, etc. To understand the importance of measurements, let us take a few examples. To decide who is the winner in a running race the time taken by runners to cover a certain distance is measured. Similarly, to determine the mileage of a vehicle, the distance travelled by it is measured. Thus, measurement of quantities play an important role in our everyday life.
In this chapter, we make an attempt to identify different physical quantities and associate them with proper units. We also discuss some important techniques used for measuring physical quantities.
PHYSICAL QUANTITIES AND THEIR UNITS
The quantities that can be measured are called physical quantities. For example, mass, length, volume, area, etc. In order to measure any physical quantity, the quantity is compared with a known standard quantity. This well defined standard quantity is called unit. For example, the unit kilogram (kg) is defined as the mass of a certain platinum-iridium block kept at the international bureau of weights and measures. Now any body having the same mass as this lump is said to have a mass of 1 kg and a body having double the mass as this lump is said to have a mass of 2 kg and so on. Hence, in order to express any physical quantity, we need to state its numerical value and the unit.
Characteristics of a Unit
A unit used to measure a physical quantity should have the following characteristics.
1. It should be well-defined.
2. It should be reproducible.
3. It should be unchangeable.
4. It should be of measurable size.
Based on their independency from other quantities, physical quantities can be classified into two categories.
Fundamental Quantity
A quantity which is independent of other quantities is called a fundamental quantity. Mass, length, time, electric current, temperature, luminous intensity and the amount of substance are the fundamental quantities.
Derived Quantity
A quantity which is dependent on other physical quantities and can be derived from the fundamental quantities is called a derived quantity. Area, volume, density, force and velocity are some examples of derived quantities.
Fundamental Unit
The unit of a fundamental quantity like mass or length is called a fundamental unit. These are kilogram, metre, second, ampere, kelvin, candela, mole.
Derived Unit
The unit of a derived quantity like volume or velocity is called a derived unit.
Example: m s–1, g cm–3, m s–2, etc.
Systems of Units
A system which defines the fundamental units, in comparison with which a fundamental quantity can be expressed is referred to as system of units. Different systems have been developed over a period of time.
The following systems of units are in common use:
1. F.P.S. system: In this system, the units of mass, length and time are pound, foot and second, respectively.
2. C.G.S. system: In this system, the units of mass, length and time are gram, centimetre and second, respectively.
3. M.K.S. system: I n this system, the units of mass, length and time are kilogram, metre and second, respectively.
4. S.I.—(Systeme International d’ unites): This system is an extended version of M.K.S system. This system has seven fundamental and two supplementary quantities. In this system the units of metre, kilogram and second have been redefined for more accuracy.
As of today S.I. system is accepted and used all over the world for scientific work.
Units and their symbols of fundamental quantities in various systems of units are tabulated as shown below. Fundamental Quantity (System of Units)
1. Length centimetre (cm) foot metre (m) metre (m)
2. Mass gram (g) pound kilogram (kg) kilogram (kg)
3. Time second (s) second (s) second (s) second (s)
4. Amount of substance – – – mole (mol)
5. Intensity of light – – – candela (cd) (Continuted)
6. Strength of electric current – – – ampere (A)
7. Temperature – – – kelvin (K)
DEFINITIONS OF UNITS
1. Metre: Initially metre was defined as one ten millionth part of the distance on the earth from the pole to the equator. As per the modern definition one metre is the length of a certain platinum-iridium rod maintained at 0ºC and kept in the International Bureau of Weights and Measures at Sevres near Paris.
(OR)
One metre is 1,650,763.73 times the wavelength of orange light emitted by a krypton atom at normal pressure.
2. Kilogram: One kilogram is the mass of a certain lump made from an alloy of platinumiridium maintained at 0ºC in the International Bureau of weights and measures.
3. Second: One second is defined as (1/86,400)th part of the mean solar day. As per the modern definition, one second is the time taken by a cesium atom (Cs133) to complete 9,192,631,770 vibrations.
MEASUREMENT OF LENGTH
Different instruments are used for measuring length depending upon the length being measured. For measuring the length of a room, width of a road, length of a piece of cloth, etc., which are larger quantities, measuring tapes may be used. But while measuring smaller lengths, like the diameter of a rod or wire, the length of a small rod, the thickness of a lamination sheet, etc., more accurate instruments need to be used. Vernier calliper is one such instrument. The accuracy with which an instrument can measure a physical quantity is determined by its least count.
Least count of an instrument is the smallest measurement that the instrument can make accurately. The least count of a metre scale is 0.1 cm.
Metre Scale
Metre scale is graduated in millimetres, i.e., its least count is 1 mm. While measuring the length of any object using a scale, the observations should be taken by keeping the eye vertically above the ends of the object. This avoids the parallax error.
FIGURE 1.1 Measuring length of a rod using a scale
To measure the length of a rod or diameter of a sphere, etc., the objects can be held between two blocks as shown in Fig. 1.2 (i) and Fig. 1.2 (ii).
FIGURE 1.2 Measuring length of a rod and diameter of a sphere using a scale and blocks
The readings x and y correspond to the positions of the two edges that hold the object.
Length of rod = y x = 2 cm 1 cm = 1 cm.
Diameter of sphere = y x = 1.7 – 0.8 cm = 0.9 cm.
Vernier Calliper
Vernier calliper is an instrument which uses a combination of two scales, main scale and vernier scale sliding over each other, such that the least count of the instrument is less than the least count of the main scale.
FIGURE 1.3 Measuring length of an object using Vernier callipers
The principle of a vernier is to make ‘N’ vernier scale divisions equal to (N – 1) main scale divisions.
DESCRIPTION
Description of Vernier Calliper
A typical vernier calliper consists of a steel strip which is generally marked in centimetres and millimetres along the lower edge. This scale is known as the main scale. The end of the main scale is provided with the fixed jaws, J1 (external jaw) on the lower side and J3 (internal jaw) on the upper side. A sliding frame with graduations marked on the lower side slides over the main steel strip; this scale is known as the vernier scale
Generally the vernier scale of a standard vernier calliper is provided with 10 graduations to coincide with 9 main scale divisions, i.e., the 10 divisions on vernier scale measure 9 mm.
The vernier frame is also provided with the movable jaws, J2 (external jaw) on the lower side and J4 (internal jaw) on the upper side.
To determine the least count of the vernier calliper:
The least count of a vernier calliper can be determined as follows:
For a standard vernier calliper, Least Count (L.C.) = 1M.S.D.
Least Count (L.C.) = 1 M.S.D. – 1 V.S.D. = 1 mm – 0.9 mm = 0.1 mm = 0.01 cm or 1mm 10 = 0.1 mm = 0.01 cm
Number of V.S.D.s
Procedure for taking measurements using a vernier calliper:
1. Determine the least count of the given calliper.
2. To measure dimensions of any object, that object should be held tightly and gently between the external jaws (for external dimensions) or with internal jaws (for inner dimensions) as shown below.
Observations to be Made
1. Main Scale Reading (M.S.R.): It is the smaller of the two values of the main scale between which the zero division of vernier scale lies.
2. Vernier Coinciding Division (V.C.D. or n): It is the vernier scale division which coincides with any one of main scale divisions. It is denoted as ‘n’.
3. Observed reading
FIGURE 1.5 Measuring lengt h of a rod using Vernier callipers
Length of the rod = y − x = (z x) + (y z) = M.S.R. + (y z)
The fraction (y z) can be determined using the Vernier scale. y z = (w z) (w y)
Let ‘n’ be the V.C.D.
Then,
(w z) = n × M.S.D. (w y) = n × V.S.D.
∴ y z = n(M.S.D. V.S.D.) = n × L.C.
∴ Length of the rod, y x = M.S.R. + n × L.C.
Thus, observed measurement = M.S.R. + n × L.C.
Measurement of Area
Area is the extent or measure of a surface. Area is a derived quantity and its units can be deduced from the units of length. The S.I. unit of area is m2 and 1 m2 = 10000 cm2
The area of regular geometrical figures like squares, rectangles, circles, triangles, etc., can be calculated by using appropriate formulae relating the areas of these figures to their length, breadth, radius, etc. For instance, the area of a square is given by A = (side)2; so by knowing the measure of the side of the square, its area can be calculated.
The area of an irregular object may be determined by tracing out the given shape on a graph sheet and counting the number of squares that the object counts. The number thus obtained will be equal to the area in mm2
