# Mathematically prove that acceleration due to the gravity of a body is independent of its mass.

From second law of motion, the force on a body is the product of its mass and acceleration.
Let the mass of body be m.

The acceleration of falling objects due to the gravitational force of earth is equal to the acceleration due to gravity(g).
Thus, force(F) on the falling objects is given by,
F=mg
This force is equal to the gravitational force between the body and earth.
where, G=Universal Gravitational constant
M=mass of earth
m=mass of body
r=distance between the body and the centre of earththe
As both forces are equal,
which is independent of mass(m) of body.

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