Explanation

(a) Acceleration due to gravity is given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g = \frac{GM}{R^{2}}$
where $G$ is gravitational constant.
$\mathbf{For\ earth:}\ g_{e} = \frac{GM_{e}}{R_{e}^{2}}$
$\mathbf{For\ planet:}\ g_{p} = \frac{GM_{p}}{R_{p}^{2}}$
$Therefore,\ \ \ \ \ \frac{g_{e}}{g_{p}} = \frac{GM_{e}/R_{e}^{2}}{GM_{p}/R_{p}^{2}}$
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{e}}{g_{p}} = \frac{M_{e}}{M_{p}}\ \times \frac{R_{p}^{2}}{R_{e}^{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
$Given,\ \ M_{p} = 2M_{e},\ \ R_{p} = 2R_{e}$
Putting the values in the Eq. (i), we obtain
$\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{e}}{g_{p}} = \frac{M_{e}}{{2M}_{e}} \times \frac{\left( 2R_{e} \right)^{2}}{R_{e}^{2}} = \frac{1}{2} \times \frac{4}{1} = 2$
$\therefore\ \ \ \ \ \ \ \ \ g_{p} = \frac{g_{e}}{2}$