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

We can simply solve this by using the concept of potential and kinetic energy where the potential energy is the energy possessed by the object because of the position relative to other objects and the kinetic energy is due to the motion of the object. When both the objects are dropped, it undergoes a freefall. Hence the net energy becomes zero. When the masses are dropped at the beginning it has potential energy which is being converted into kinetic energy.

Complete step-by-step solution:
According to the law of conservation of energy we can get
Potential energy $=$ Kinetic energy
$mgh = \,\dfrac{1}{2}m{v^2}$
$v = \sqrt {2gh}$
Since velocity is not dependent on mass, both the balls reach the ground at the same time.
Hence the answer is an option (D) (equal to $t$).

All the bodies are attracted towards the earth by the same force. Here the masses are very negligible compared to the mass of earth, they will reach the ground at the same time if we neglect air drag. If air drag occurs then the one with higher density will reach first. If the masses can be compared to the mass of the earth, the one with higher mass will touch the earth’s surface first.

Note: Different materials have different densities which direct the quantities required for achieving specific masses. Freefall can be defined as the motion of anybody in which only the gravitational force is acting on it. In the case of general relativity, the gravitation phenomenon can be reduced to space-time curvature. Here a body in free fall has null forces acting on it.