CBSE Class 9 Science Gravitation Exam Notes

CBSE Class 9 Science Gravitation Exam Notes. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

                                                                 FORCE OF GRAVITATION

Any two particles in the universe attract each other. This force is called the force of gravitation.  This concept was given by Newton.

NEWTON’S LAW OF GRAVITATION

According to newton, "Any two bodies in universe attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

Mathematical expression

Let A and B be two particle of mass m₁ and m₂ respectively. Let the distance AB = r. By the law of gravitational, the particle A attracts the particle B with a force F such that.

Here G is a constant known as the universal constant of gravitation. G = 6.67 × 10^–11 Nm²/kg²

*G is independent of the masses of the bodies and the distance between them.

*Newton's law of gravitation is applicable for everybody in the universe.

Note : The force between any two bodies in the universe is called the force of gravitation while the force with which earth attracts a body is called the force of gravity.

 Some Scientific Phenomenon Based on Gravitational Force :

• The gravitational force between the sun and the earth keeps the earth moving around the sun.

• The gravitational force b/w the earth and the moon keeps the moon moving around the earth.

• Existence of our solar system is due to gravitational force.

• Gravitation force of the sun and the moon on the earth's water surface is responsible for the tides in sea.

• Atmosphere above the earth is held due to gravitational force of the earth.

• Gravitational force between the sun and planet keeps the planet moving around the sun.

• Gravitational force is responsible for providing the centripetal force required by the planets.

• The attractive force of the earth is responsible for providing the centripetal force required by moon.

Newton's Third Law of Motion and Law of Gravitation :

• Newton's third law of motion is applicable to gravitation also.

Ex. if the earth exerts a force of attraction on a body, the body also exerts an equal and opposite force of attraction on the earth.

• As a = F/m

mass of the body is larger, acceleration produced will be smaller and vice versa.

Ex. 1 Calculate the force between two masses of 100 kg and 1000 kg separated by a distance of 10 m (G = 6.67 × 10^–11 Nm²/kg2).

Sol. According to Newton's law of gravitation, force of attraction between two bodies is

F = Gm₁m₂ /r ²

Here, m₁ = 100 kg; m₂ = 1000 kg ;

r = 10 m ; G = 6.67 × 10–11Nm²/kg2

\ F = 6.67 x 10^–11 x 100 x 1000 / (10)²

= 6.67 × 10^–8 N

Ex. 2 Given mass of earth = 6 × 10²⁴ kg, radius of earth = 6.4 × 10⁶ m. Calculate the force of attraction experienced by a man of mass 50 kg.

Sol. Force of gravitation is given by the expression, F =  Gm₁m₂ /r ²

Here, mass of earth, m1 = 6 × 10²⁴ kg;

mass of man, m2 = 50 kg

Distance between them is to be taken equal to the radius of earth.

 r = 6.4 × 106 m

Substituting these values, we get

F = 6.67 x10^–11 x 6 x10²⁴ x 50/ (6.4 x 10⁶ )² = 488.5 N

Ex. 3 Compare the gravitational forces exerted by the sun and the moon on earth. Which exerts a greater force on earth ?

(Given : mass of sun, Ms = 4 × 10³¹ kg; mass of moon, Mm = 6.3 × 10²² kg; distance between sun and earth, rse=1.3× 10¹² m and the distance between moon and earth, rme= 4.5 × 10⁸m)

Sol. If mass of sun is Ms and mass of earth is Me and distance between the sun and earth is rse, then force exerted by the sun on earth is 

then force exerted by the sun on earth is

Ex. 4 If mass and radius of earth is 6.0 × 10²⁴ kg and 6.4 × 10⁶ m respectively, calculate the force exerted by earth on a body of mass

1 kg. Also, calculate :

(i) acceleration produced in the body of mass

1 kg, and

(ii) acceleration produced in the earth

Sol. From Newton's law of gravitation, we know that the force of attraction between two bodies is given by

F = Gm₁m₂ /r ²

Here, m₁ = mass of earth = 6.0 × 10²⁴ kg;

m₂ = mass of body = 1 kg

r = distance between the two bodies

= radius of earth = 6.4 × 106 m

G = 6.67 × 10^–11 Nm₂/kg2

\ F = 6.67 x10^–11 x 6.0 x10²⁴ x 1 / (6.4 x10⁶ )2 = 9.8 N

This shows that earth exerts a force of 9.8 N on a body of mass of 1 kg. The body will exert an equal force of attraction of 9.8 N on earth.

(i) Acceleration produced in the body of mass 1kg

Force = mass × acceleration

\ Acceleration, a =F /m= 9.8/1 = 9.8 m/s2

Thus, the acceleration produced in a body of mass 1 kg due to attraction of earth is

9.8 m/s2, which is quite large. Thus, when a body is released, it falls towards the earth with an acceleration of 9.8 m/s2, which can be easily observed.

(ii) Acceleration produced in the earth

Similarly, acceleration of earth is given by

= Force /M assof eart h =9.8/ 6.0 ´10²⁴

= 1.63 × 10-²⁴ m/s2

This shows that the acceleration produced in the earth by a body of mass 1 kg is

1.63 × 10-²⁴ m/s2 which is very small and cannot be observed.

Ø EARTH'S GRAVITATIONAL FORCE

 The force which earth exerts on a body is called 'force of gravity'. i.e. F =

GM m/R 2

Where M = mass of the earth, R = radius of the earth.

 Due to this force, a body released from some height on the earth's surface falls towards the earth with its velocity increasing at a constant rate.

 Acceleration due to Gravity : The acceleration produced in a body due to attraction of earth is called the acceleration due to gravity and is denoted by 'g'.

g = GM/R 2 = 9.8 m/s2

near the earth surface

g on moon » g e/6 = 9.8/6 m/s2

 A body moving upwards with some initial velocity, experiences a retardation of

9.8 m/s2 & its velocity decreases continuously unless it becomes zero.

 After this, it again starts falling towards the earth with the same acceleration of 9.8 m/s2.

 The value of g is minimum at equator and maximum at poles.

 The value of g does not depend upon the mass of the body falling towards the earth.

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