The amount of work done to raise a mass ' m ' from the surface of...

Initial potential energy at the surface of the Earth is $U_i = -\dfrac{GMm}{R}$

Final potential energy at height $h = R$ is $U_f = -\dfrac{GMm}{R + R} = -\dfrac{GMm}{2R}$

Work done $W = \Delta U = U_f - U_i$

$W = -\dfrac{GMm}{2R} - \left(-\dfrac{GMm}{R}\right) = \dfrac{GMm}{2R}$

Using the relation $g = \dfrac{GM}{R^2}$, we get $GM = gR^2$

Substituting this in the expression for work done:

$W = \dfrac{gR^2 m}{2R} = mg\dfrac{R}{2}$

Answer: $mg\dfrac{R}{2}$