Question

Two different masses are dropped from the same height for their downward journey under gravity. The larger mass reaches the ground in time t. The smaller mass takes time
(A) Equal to $\sqrt t $
(B) Greater than t
(C) Less than t
(D) Equal to t

Answer 1

Hint: Let's solve this question using the concept of kinetic energy and potential energy.
Kinetic energy: It is the energy possessed by an object due to its motion.
Potential energy: It is the energy possessed by an object because of its position relative to other subjects.
Here two masses are dropped from a certain height they are experiencing freefall.
When the ball is at rest the net energy is zero. As the ball is dropped initially there is potential energy and later it is converted into kinetic energy.

Complete step by step solution:
According to the law of conservation of energy.
Potential energy $ = $ Kinetic energy
$ \Rightarrow mgh = \dfrac{1}{2}m{v^2}$
$ \Rightarrow v = \sqrt {2gh} $
Since velocity is independent of mass both of the balls reach the ground at the same time.

Hence the correct answer is option D.

Additional Information:
 Potential energy are of two types mainly. Gravitational potential energy and Elastic Potential energy.
Gravitational Potential Energy can be defined as energy obtained by an object in a gravitational field when there is a change in the position of the object.
Gravitational Potential is the amount of work done in moving a unit test mass from some defined position to a position of zero potential, usually infinity.
Elastic Potential energy: When an elastic object is compressed or stretched by an external force the energy stored is elastic potential energy. According to Hooke's law the amount of stretching will be directly proportional to the force applied.

Note: Free fall is defined as any motion of a body where gravity is the only force acting upon it. In the case of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting upon it.