Question

prove that acceleration due to gravity is independent of mass of the falling body

Answer 1

Consider the earth to be spherical body⚪ of mass 'M' and Radius 'R' with centre 'O'.

Suppose a body of mass 'm' is placed on the surface of earth where acceleration due to gravity is 'g'.

The earth behaves as if the whole mass is concentrated on its centre 'O'.

Let F be the force of attraction between the earth and the body.

According to Newton's Universal law of gravitation

F = GMm/R^2 --------------> 1

This force exerted by the earth produces an acceleration in the body due to which the body moves downwards⬇

According to second law of motion:-

F = ma

The acceleration produced by the earth is known as Acceleration due to gravity and it is represented by 'g' symbol. So, by writing 'g' in place of 'a' in above equation, we get

F = mg ----------------> 2

mg = GMm/R^2

g = GM/R^2 ----------------> 3

So, From equation (3) we note that the value of acceleration due to gravity 'g' is independent of mass, shape and size of the body but depends upon the mass and radius of the earth.

Hope my answer helps you :)

Regards,
Shobana

Answer 2

Answer:

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Explanation: