What is potential energy? Derive an expression for the gravitational potential energy.

The energy possessed by a body by virtue of its position is called potential energy.
Expression : Consider a body of mass (m) on the ground. It is lifted vertically upwards through a height (h).
The gravitational force acting on the body = mg.
The work done by the external force against gravitational force is

$\begin{array}{l}\mathrm{W}=\mathrm{Fscos\theta }\\ =\mathrm{Fscos}0(\because \mathrm{\theta }=0)\\ =\mathrm{Fs}\\ =\mathrm{mgh}\\ (\therefore \mathrm{F}=\mathrm{mg}\text{ and }\mathrm{s}=\mathrm{h})\end{array}$
This work is stored as potential energy of the body.
$\therefore$ Potential energy of the body U = mgh