The work required to move a body of mass m from the surface of the Earth (radius R ) to infinity is W . The work required to move the same body from the surface of the Earth to a height h = R above the surface is

Step-by-step solution

The work done to move a body from the surface of the Earth to infinity is equal to the change in its gravitational potential energy: W = U_ - U_ surface = 0 - (- GMm R ) = GMm R The work done to move the body from the surface to a height h = R is: W' = U_ final - U_ initial = - GMm R+R - (- GMm R ) W' = - GMm 2R + GMm R = GMm 2R Comparing the two expressions, we get: W' = 1 2 ( GMm R ) = W 2 Answer: W 2