Explanation

(c) The value of acceleration due to gravity changes with height $(ie,\ altitude)$. If $g'$ is the acceleration due to gravity at a point, at height $h$ above the surface of earth, then
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g^{'} = \frac{GM}{(R + h)^{2}}$
$but,\ \ \ \ \ \ \ \ \ \ \ \ \ \ g = \frac{GM}{R^{2}}$
$\therefore\ \ \ \frac{g^{'}}{g} = \frac{GM}{(R + h)^{2}} \times \frac{R^{2}}{GM} = \frac{R^{2}}{(R + h)^{2}}$
$Here,\ \ \ g^{'} = \frac{GM}{(R + h)^{2}} = \frac{GM}{(R + 3R)^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{GM}{(4R)^{2}} = \frac{GM}{{16R}^{2}} = \frac{g_{e}}{16}$