Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.

Explanation

The gravitational potential energy (U) at some height h is equal to the aount of work required to take the object from the ground to that height h.
`U=intvecF_(a),dvecr=underset(0)overset(h)int|vecF_(a)||dvecr|costheta`
If the displacement and the applied force are in the same upward direction then, the angle betweeen them is `theta=0^(@)`. Since, `cos0^(@)=1and|vecF_(a)|=mgand|dvecr|=dr`
`U=mgunderset(0)oversethintdrimpliesmg[r]_(0)^(h)=mgh`