Show mathematically that the acceleration experienced by an object during free fall is independent of the mass of the object.

(N/A) Let us consider an object of mass $m$ near the surface of a planet of mass $M$ and radius $R.$
According to the universal law of gravitation,the gravitational force $F$ acting on the object is given by:
$F = \frac{GMm}{R^2} \dots (1)$
According to Newton's second law of motion,the force $F$ acting on an object of mass $m$ is:
$F = mg \dots (2)$
(where $g$ is the acceleration due to gravity).
By equating equations $(1)$ and $(2)$,we get:
$mg = \frac{GMm}{R^2}$
Dividing both sides by $m$,we obtain:
$g = \frac{GM}{R^2}$
Since the mass of the object $m$ cancels out,the acceleration due to gravity $g$ depends only on the mass of the planet $M$ and its radius $R$. Thus,the acceleration experienced by an object during free fall is independent of its mass.