Find the change in the gravitational potential energy when a body of mass `m` is raised to a height nR above the surface of the earth. (Here, R is the radius of the earth)

Explanation

Gravitational potential energy of mass `m` at earth's surface
`U_(e)=-(GMm)/(R)`
Gravitational potential energy of same mass at a height nR from the earth's surface
`U_(h)=-(GMm)/((R+nR))=-(GMm)/(R(n+1))`
Thus, magnitude of the change in gravitational potential energy
`DeltaU=U_(h)-U_(e)`
`=(GMm)/(R){1-(1)/((n+1))}`
`=((n)/(n+1))((GMm)/(R))=((n)/(n+1))mgR" "(because GM=gR^(2))`.