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 is (here R is the radius of the earth).

The correct option is A (nn+1)mgR
Gravitational potential energy of mass m at any point at a distance r from the centre of earth is
U=−GMmr
At the surface of earth r=R, ∴Us=−GMmR=−mgR (∵g=GMR2)
At the height h=nR from the surface of earth r=R+h=R+nR=R(1+n)
∴Uh=−GMmR(1+n)=−mgR(1+n)
Change in gravitational potential energy is
ΔU=Uh−Us=−mgR(1+n)−(−mgR)=−mgR1+n+mgR=mgR(1−n)=nmgR(1+n).