Question

If a stone and a pencil are dropped simultaneously in vacuum from top of a tower, which of the two will reach the ground first?

Answer 1

Hint When two objects of different masses are dropped in vacuum, then there will not be any kind of air resistance acting on them. That means the only force acting on them would be the gravitational force.

Complete step by step answer
We know that, when two objects of different masses are dropped from top of a tower, in vacuum, the air drag or resistance would not be acting on them. Thus, the objects will be accelerating with the acceleration due to gravity, towards the earth’s surface.
But as we know that the acceleration due to gravity is given by:
 $\Rightarrow g = \dfrac{{GM}}{{{r^2}}} $ where $ G $ is the universal gravitational constant, $ M $ is the mass of earth and $ r $ is the radius of earth. So, from this formula it can be understood that the acceleration due to gravity is constant at the same distance from the earth’s surface and it is independent of the masses of the objects.
Thus, we can elucidate that both pencil and stone would be experiencing only gravitational force and they accelerate towards the earth with a constant acceleration equal to the acceleration due to gravity. Therefore, we can conclude that when dropped from a height, but in vacuum, both the stone and the pencil will reach the ground simultaneously. So, the correct answer is that they will reach the ground at the same time.

Note
This phenomenon of falling bodies in the absence of any force other than the gravitational force is called free fall. If someone is under free fall, experiences weightlessness and this is also experienced when the gravitational field is very weak.