The amount of work done to raise a mass ' m ' from the surface of the Earth to a height equal to the radius of the Earth ' R ', will be :

Step-by-step solution

Initial potential energy at the surface of the Earth is U_i = - GMm R Final potential energy at height h = R is U_f = - GMm R + R = - GMm 2R Work done W = U = U_f - U_i W = - GMm 2R - (- GMm R ) = GMm 2R Using the relation g = GM R^2 , we get GM = gR^2 Substituting this in the expression for work done: W = gR^2 m 2R = mg R 2 Answer: mg R 2