Physics for students of class IX
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CONTENTS Chapter 1
Motion
7
Chapter 2
Force and Laws of Motion
41
Chapter 3
Gravitation and Fluids
77
Chapter 4
Work and Energy
109
Chapter 5
Sound
135
The following 3 pages will give you a glimpse of how effectively we have used illustrations along with simple language to explain a concept. The following pages are from the part of the physics book for IX grade, these pages detail “Universal Law of Gravitation�
If the masses of two bodies are small, then the gravitational force between them will be very weak. For example, two stones lying on the ground also attract each other (figure 3). However, since their masses are small, the gravitational force of attraction between them will be very weak. Hence, we do Figure 3: Gravitational force between not observe them moving towards two stones each other.
Moon has no atmosphere because the gravitational force exerted by it is very small.
Gravitational force or gravity is always a force of attraction. It is a universal force. All massive bodies in the universe attract each other with gravitational force. In our solar system, planets revolve around the sun under the effect of sun’s gravitational force.
Universal Law of Gravitation The universal law of gravitation and the three laws of motion were given by Sir Isaac Newton in his treatise Philosophiae Naturalis Principia Mathematica. Hence, the universal law of gravitation is also known as Newton’s law of gravitation. According to this law: Any two massive bodies in the universe attract each other with gravitational force. The magnitude of this force is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. Newton’s law of gravitation is known as universal law of gravitation because it is applicable to all bodies having mass. Suppose two bodies A and B having masses m1 and m2 are placed at a distance r from each other. If the force of gravitational attraction between them is F, then according to the universal law of gravitation: F ∝ m1 × m2
… (1)
… (2)
[Note: Equation (2) is also known as the inverse square rule. You will learn more about this rule later] On combining equations (1) and (2), we get PHYSICS
… (3)
78 Score ‘n’ Learn
⇒
… (4)
Here, G is the constant of proportionality. It is known as the universal gravitational constant.
Meet the Scientist: Sir Isaac Newton
Sir Isaac Newton, the English mathematician and physicist, was born at Woolsthorpe, near Grantham in Lincolnshire. He joined Cambridge University in 1661. He became a fellow of Trinity College in 1667 Meet the Scientist and Lucasian Professor of Mathematics in 1669. He was at the university till 1696. The famous Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) was prepared during the years 1665-1666. The Principia, as it is commonly known, was not published until 1687. For nearly 300 years, Newton has been considered as the exemplar of modern physical science. His Figure 4: Sir Isaac accomplishments in mathematical research are as Newton innovative as those in experimental investigations. He is also known for his works on chemistry, the early history of Western civilisation, and theology. Notable among his studies is the investigation of the form and dimensions of Jerusalem’s Solomon’s Temple, as described in the Bible.
It is a common misconception that the gravity of earth ceases to exist beyond its atmosphere. However, this is incorrect. Earth exerts gravitational force beyond its atmosphere also, but the effect of this force is very less. It is the gravitational force between the moon and earth that keeps the moon in an orbit around earth.
The Universal Gravitational Constant According to the universal law of gravitation, the gravitational force F between two bodies having masses m1 and m2, placed at a distance r from each other, is given by
, where G is the universal gravitational constant
On rearranging this expression, we get
… (5)
Can you determine the SI unit of universal gravitational constant from this equation? The SI unit of r is m; the SI unit of F is N; and the SI unit of m1 and m2 is
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kg. Using these in equation (5), we can determine the SI unit of universal gravitational constant as [G] = Let us now determine the value of universal gravitational constant. If the masses m1 and m2 are 1 kg each and the distance r between them is 1 m, then equation (4) reduces to F = G, i.e., the universal gravitational constant G is numerically equal to the force of gravitation that exists between two bodies of unit mass kept at unit distance from each other. The value of universal gravitational constant, G, was first determined by Cavendish through the torsion bar experiment. The apparatus of this experiment comprises two pairs of spheres. Each pair Figure 5: Cavendish experiment of spheres forms a dumbbell having a common axis (figure 5). One of the dumb-bells is suspended from a quartz fibre and rotates freely when the fibre is twisted. The position of a reflected light spot from a mirror attached to the fibre gives the measure of the amount of twists. The second dumb-bell can be swivelled in such a way that each of its spheres is close to one of the spheres of the other dumb-bell. The gravitational attraction between the two pairs of spheres twists the fibre and the magnitude of the force of gravity is calculated by measuring the amount of twists in the fibre. The value of G, as determined by Cavendish, came out to be 6.67 × 10–11 Nm2/ kg2.
In order to measure the density of Earth, Rev. John Michell came up with an idea in 1795 that is today known as the Cavendish experiment. The apparatus used in this experiment was modified by Henry Cavendish in 1798 to measure the value of G.
Importance of the Universal Law of Gravitation
The universal law of gravitation helps us understand several natural phenomena. Some of these are: Dropped objects falling towards Earth Earth pulls all objects towards itself with gravitational force. Hence, when an object is dropped, it falls towards earth. Revolution of moon around Earth Moon is attracted by Earth’s gravitational force. This keeps moon revolving around Earth in its orbit of movement. PHYSICS
80 Score ‘n’ Learn
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