Explanation

(b) Gravitational force on a body at a distance $x$ from the centre of earth $F = \frac{GMm}{x^{2}}$
Work done,
$W = \int_{R}^{R + h}{F\ dx = \int_{R}^{R + h}{\frac{GM\ m}{x^{2}}dx}}$
$= GMm\left\lbrack - \frac{1}{x} \right\rbrack_{R}^{R + h} = mgR^{2}\left\lbrack \frac{1}{R} - \frac{1}{R + h} \right\rbrack$
This work done appears as increase in potential energy
$\mathrm{\Delta}E_{p} = mgR^{2}\left\lbrack \frac{1}{R} - \frac{1}{R + h} \right\rbrack$
$= mg(5h)^{2}\left\lbrack \frac{1}{5h} - \frac{1}{6h} \right\rbrack = \frac{5}{6}mgh$