The change in the gravitational potential energy when a body of mass m is raised to a height n R above the surface of the earth is (here R is the radius of the earth)

Step-by-step solution

Gravitational potential energ at any point at a distance r from the centre of earth is U=- G M m r At the surface of earth r=R , U_s=- G M m R =-m g R ( g= G M R^2 ) At the height h=n R from the surface of earth r=R+h=R+n R=R(1+n) U_h=- G M m R(1+n) =- m g R (1+n) Change in gravitational potential energy is aligned U & =U_h-U_s=- m g R (1+n) -(-m g R) & =- m g R 1+n +m g R aligned =m g R (1- 1 1+n )=m g R ( n 1+n )