Prove that the acceleration due to gravity is independent to

the mass of the falling body

The force of gravity on an object increases with its mass; thus, the acceleration of gravity is constant.

Explanation:

one can prove this by plugging in values to Newton's 2nd law equation

F = ma, or by using the formula to calculate the force of gravity.

Force of Gravity = GMm/r^2

with G being the gravitational constant, M the mass of the earth, m the mass of the falling body, and r the distance from the earth's center.

Force of Gravity can be written as mg, with g being the acceleration due to gravity.

As we can see, m cancels on both sides, leaving

g = GM/r^2

Generally in physics problems, r will be treated as constant to achieve

g = 9.8m/s^2