Question

Does free falling depend on the mass of an object? Does acceleration depend on the mass of an object??

Answer 1

Dear student,
We know $F=ma$
Acceleration due to gravity is given by
$$\begin{gathered} a=\frac{F}{m} \\ a=\frac{mg}{m}=g \\ a=g \end{gathered}$$
The acceleration or the rate at which it falls does not depend on the mass of object

For an object of mass m in the gravitational field to to the body of mass M,the gravitational force is given by
$F=\frac{GMm}{R^2}$,G is gravitational constant and r is the distance between the two mass.
We know $F=mass\times acceleration$
Acceleration of mass m due to gravity is $\frac{GM}{r^2}$
Acceleration of mass M due to gravity is $\frac{Gm}{r^2}$
So the acceleration of given mass due to gravity does not depend upon its own mass,But it depends upon the mass exerting gravitational force.

Regards.