A body of mass is taken from earth surface to the height h equal to twice the radius of earth ( R e ) , the increase in potential energy will be : ( g = acceleration due to gravity on the surface of earth)

Step-by-step solution

The potential energy of a particle at a distance r   ( > R e ) from the centre of Earth is, U = - G M e m r Initially, the particle is at a height R e from the surface. Therefore, r = R e . ∴ U i = - G M e m R e When height is increased to 2 R e from surface, r = 2 R e + R e = 3 R e ∴ U f = - G M e m 3 R e Thus, the change in potential energy is ∆ U = U f - U i = - G M e m 3 R e + G M e m R e = 2 3 G M e m R e = 2 3 G M e R e 2 m R e = 2 3 m g R e   as   g = G M e R e 2