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

Derive an expression for the gravitational potential energy of a body

1.	Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.
Answer» SOLUTION :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`