# Acceleration due to gravity of a body is independent of its mass-How to Show mathematically?

Acceleration due to gravity of a body is independent of its mass – let’s show it mathematically.

We will consider a body of mass m on the surface of the earth. Let M be the mass of the earth and R be the distance between the body and the centre of the earth (when the radius of the earth is R). Let g be the acceleration due to gravity. And say, F is the force acting on the body.

According to Newton’s second law of motion,
F = mg …………………………..(1)

And, According to Newton’s Law of Gravitation,
F = GMm/R2 ……………………(2)

From (1) and (2),

mg = GMm/R2

=> g = GM/R2 ………………….(3)

From equation (3) we can see that the expression of g doesn’t have any mention of m (mass of the body).
Thus, It’s clear that, Acceleration due to gravity g of a body is independent of its mass.

Acceleration due to gravity of a body is independent of its mass-How to Show mathematically?
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