Explanation

(b) $\frac{g_{e}}{g_{m}} = \frac{R_{e}\rho_{e}}{R_{m}\rho_{m}} = \frac{2}{3} \times \frac{4}{1} = 6\ or\ \ g_{m} = \frac{g_{e}}{6}$
For motion on earth, using the relation,
$s = ut + \frac{1}{2}at^{2}$
We have, $\frac{1}{2} = 0 + \frac{1}{2} \times 9.8r^{2}$ or $t = 1/\sqrt{9.8}s$
For motion on moon, $3 = 0 + \frac{1}{2}(9.8/6)t_{1}^{2}$
or $t_{1} = 6\sqrt{9.8}s$ $\therefore\frac{t_{1}}{t} = 6$ or $t_{1} = 6t$