Question

Derive expression for gravitational potential energy for a body placed at a height above the ground.

Answer 1

Derivation of Expression [U = mgh].

Assume that a mass m body is raised to a vertical height h from the earth's surface.

Without acceleration, the force (mg) needed to raise the body is equal to the force of gravity pulling it down vertically.

Work done to lift body from A to B

W = Force of gravity × Displacement above the ground

= mg × h

W = mgh

This work is stored as gravitational potential energy within the body.