Hello everyone, here we are going to discuss about the acceleration that is caused due to force of gravity. Have you noticed that while catching the ball coming from higher altitude gets down faster when reaches close to you? If any object is falling towards the earth, speed of object is constant or changing? All these questions has the same reason i.e. acceleration due to gravity.
Earth exerts the force on every object towards its centre; we called it as gravitational force. This force causes acceleration, termed as gravitational acceleration or acceleration due to gravity denoted by ‘g’. Let us derive the formula for it.
Consider a body of mass ‘m’ situated on the surface of the earth of mass ‘M’ and radius ‘R’. Then according to Newton’s law of gravitation, the gravitational force acting between earth and object will be,
Gravitational force = G Mm/R2 …….. (1)
The weight of the body given as,
Weight of the body = mg ………(2)
The weight of the body is nothing but the force exerted on the earth hence it is always equal to the gravitational force acting on it.
mg = G Mm/R2
∴g = GM/R2 ……..(3)
Or GM = gR2
If the body is at height ‘h’ above the earth’s surface. Let gh be the acceleration due to gravity.
Gravitational force = G Mm/(R + h)2
For earth, M = 6 x 1024 kg, R = 6.4 x 106 m
Then value of ‘g’ for earth is,
g ≈ 9.8 m/s2
Important:
1) The value of ‘g’ decreases as body rises from the surface of the earth.
2) From equation (3) It is clear that the value of g is inversely proportional to square of radius of the earth. The earth is not perfect sphere. It is an elliptical at equator and flattered at the pole. The value of ‘R’ is greater at the equator; therefore, the value of ‘g’ is least at the equator. Also the value of ‘R’ is least the poles therefore ‘g’ is maximum at the poles.
Consider following examples for more detail illustration of acceleration due to gravity.
1.) Find the acceleration due to gravity on the surface of star of mass 1.2 x 106 kg and diameter of 2400 m.
Solution: