Question

Two different masses are dropped from same heights, when just these strike the ground, the following is same
(A) Kinetic Energy
(B) Potential Energy
(C) Linear Momentum
(D) Acceleration

Answer 1

Hint : Understand the factors that affect the gravitational force and time. We know that height is one of the factors that affect the time to land while dropping. Use this logic and deduce the answer.

Complete step by step answer
Acceleration due to gravity is content all around the earth. So if a ball is dropped from the second floor of the building and a pebble is dropped from the same floor of the building, let’s find out what remains constant.
Now if the masses are different, rather the height is the same let’s find what remains constant. Now , the kinetic energy of the object is given as , $ \dfrac{1}{2}m{v^2} $ . Here we can see that the kinetic energy depends upon the mass of the object and hence will differ due to change in mass of objects. Thus kinetic energy won’t remain the same for both the objects.
Now, let’s calculate potential energy. The potential energy of an object, when dropped for height h, is given as $ PE = mgh $ . Now, from the equation, we can see that the potential energy of the objects depends upon the mass of the object and the height at which it is dropped. Since the masses of the object are different, the potential energy of the objects will also be different from each other.
Linear momentum of the object is given using the formula, $ P = mv $ , where m is the mass of the object and v is the velocity of the object. Here also, the momentum depends upon the mass of the object, which makes it different for both the objects.
Out of all, only the gravitational acceleration remains constant, since at any point of earth, when 2 objects are dropped from any height, its downward acceleration will be earth’s gravitational force G. Thus the acceleration caused due to this is constant throughout. Hence, acceleration remains the same for both objects.
Hence, Option (D) is the right answer.

Note
A similar experiment was performed by astrophysicist Galileo to understand the basics of gravity. He found out that at a given location and in absence of air resistance, the objects fall under uniform acceleration.