Define 'acceleration due to gravity of earth'. Does the acceleration produced in a freely falling body depend on the mass of the body? Justify your answer mathematically.

(N/A) Acceleration due to gravity is the uniform acceleration produced in a body falling freely towards the surface of the earth due to the gravitational pull of the earth.
No,the acceleration produced in a freely falling body does not depend on the mass of the body.
According to Newton's second law of motion,the force $F$ acting on a body of mass $m$ is given by:
$F = m \times g$ --- $(1)$
According to Newton's law of universal gravitation,the gravitational force $F$ between the earth (mass $M$) and the body (mass $m$) at a distance $R$ (radius of earth) is:
$F = \frac{G M m}{R^2}$ --- $(2)$
Equating $(1)$ and $(2)$:
$m \times g = \frac{G M m}{R^2}$
Dividing both sides by $m$:
$g = \frac{G M}{R^2}$
Here,$G$ is the universal gravitational constant,$M$ is the mass of the earth,and $R$ is the radius of the earth. Since the expression for $g$ does not contain the mass of the falling body $(m)$,it proves that the acceleration due to gravity is independent of the mass of the body.