Question

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

Answer 1

Correct option is C. $$\dfrac{1}{2} mgR$$
Initial potential energy at earths surface is
$$U_i = \dfrac{-GMm}{R}$$
Final potential energy at height h = R
$$U_f = \dfrac{-GMm}{2R}$$
As work done = change in PE
$$\therefore W = U_f - U_i$$
$$= \dfrac{GMm}{2R} $$

$$(\because GM = gR^2)$$

$$= \dfrac{gR^2m}{2R} = \dfrac{mgR}{2}$$