Question

A body is falling freely under the action of gravity alone in vacuum which of the following quantities remains constant during the fall.
(A) Kinetic energy
(B) Potential energy
(C) Total mechanical energy
(D) Total linear momentum

Answer 1

Hint: When a body falls freely under the action of gravity alone in vacuum, potential energy decreases continuously and kinetic energy increases continuously, hence the conservative force acts on the body. So that total mechanical energy remains constant during their journey in vacuum. Generally, Mechanical energy is the sum of kinetic energy and potential energy.

Complete answer:
Let discuss, the total mechanical energy at point A,
  $ {E_A} = K.E. + P.E. $
 $ {E_A} = \dfrac{1}{2}m{v^2} + mgh $
At point A, velocity will be zero, hence
 $ {E_A} = 0 + mgh $
 $ {E_A} = mgh $
Total Mechanical Energy at point B,
 $ {E_B} = \dfrac{1}{2}m{v^2} + mgh $
Velocity at point B, $ v = $ and Travelled height = h
 $ {E_C} = mgh $
 $ {E_B} = \dfrac{1}{2}m \times 2gh + mg(H - mgh) $
 $ {E_B} = mgh + mgH - mgh $
 $ {E_B} = mgH $
Total Mechanical Energy at point C,
 $ {E_C} = \dfrac{1}{2}m{v^2} + mgh $
Velocity at point C, $ v = $ But Travelled Height = 0
 $ {E_C} = \dfrac{1}{2}m(2gh) + mg(0) $
 $ {E_C} = mgh $
Hence, the correct option is C (Total Mechanical Energy). As per the point A, point B and Point C; the total mechanical energy of the body will remain constant in vacuum, if we neglect the air friction.

Note:
Energy is the ability to do work, it may be in any form. The amount of energy used by a body at any work’s amount that is the released energy from that body.
S.I. unit of energy = Joule or Newton meter which means that anybody moves one meter using one Newton Force. Energy is a Scalar quantity.
Kinetic Energy: The energy of a body because of its motion, that energy is called kinetic energy.
Potential Energy: The energy of a body because of its rest on a surface and also the influence of gravity.