A body is falling freely under the action of gravity alone...

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

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Key Concepts

Conservation of Mechanical Energy

This principle states that in an isolated system where only conservative forces (such as gravity) are acting, the total mechanical energy—defined as the sum of potential and kinetic energies—remains constant over time. Energy may be converted from one form to another (for example, from gravitational potential energy to kinetic energy in free fall), but the total amount of mechanical energy does not change.

Transformation of Potential and Kinetic Energy

In a gravitational field, an object’s potential energy depends on its height, while its kinetic energy is related to its speed. As an object falls, its gravitational potential energy decreases while its kinetic energy increases, due to the conversion of energy. However, neither the potential energy nor the kinetic energy remains constant individually during the fall; it is only their sum that is conserved.

Conservation of Linear Momentum

Linear momentum remains constant only in a system where no net external force acts. In scenarios involving gravity, an external gravitational force acts on the object, which causes its momentum to change over time. This contrasts with mechanical energy conservation, which holds in the case of conservative forces.

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