Question

Derive the expression for gravitational potential energy.$Ep=mgh$

Answer 1

Step 1: Gravitational potential energy

Gravitational potential energy is the energy possessed by the body due to its position with respect to the surface of earth ( assuming surface as zero potential)

Step 2: Derivation

Let us consider a body of mass m. Let the body be raised to a height h above the ground.

The work done in raising the body to height h against the gravitational field of the earth is

$w=fh\dots .\left(1\right)$

As $f=mg\dots .\left(2\right)$

Therefore from equations (1) and (2), we get,

$w=mgh$

The work done is stored in the body in the form of gravitational potential energy.

$i.e.,E_p=w$

Therefore,

$E_p=mgh$

Hence,$E_p=mgh$ is the expression for gravitational potential energy.