Explanation

(d) Acceleration due to gravity on earth is given by $g = \frac{GM}{R^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( Here,\ M_{m} = \frac{M_{e}}{9},R_{m} = \frac{R_{e}}{2} \right)$
$Hence,\ \ \ \ \ \ \ \ \ \frac{g_{e}}{g_{m}} = \frac{M_{e}}{M_{m}} \times \frac{R_{m}^{2}}{R_{e}^{2}} = \frac{9M_{e}}{M_{e}} \times \left( \frac{R_{e}}{2R_{e}} \right)^{2}$
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{e}}{g_{m}} = \frac{9}{4}$
$So,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{m}}{g_{e}} = \frac{4}{9}$
$\because\ \ Weight\ of\ body\ on\ moon$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = weight\ of\ body\ on\ earth \times g_{m}/g_{e}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 90 \times \frac{4}{9} = 90 \times \frac{4}{9} = 40kg$