Q:

Why bodies with different masses reach gound at the same time in vacuum?

According to Newton's Gravitation Equation $$F=G \dfrac{M\cdot m}{r^2}$$ force of gravity depends upon mass of both objects, and $$F=ma$$ means force is proportional to acceleration. Then why do objects with different masses reach the ground at the same time in vacuum?

A:

The time it takes to reach the ground is determined by the acceleration of the object. If both objects accelerate in exactly the same way, then both will reach the ground at the same time.
We can easily derive the acceleration in this case, which is:
$$a=\frac{F}{m}=\frac{\frac{GMm}{r^2}}{m}=\frac{GM}{r^2}$$
As you can see, the mass $m$ of the object completely cancels out, so the acceleration depends only on the mass of the Earth (or other gravitating planet) and the distance from the center. The object's mass simply doesn't matter.

