Explanation

(a) The acceleration due to gravity $(g)$ is given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g = \frac{GM}{R^{2}}$
where $M$ is mass, $G$ the gravitational constant and $R$ the radius.
Since, planets have a spherical shape
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = \frac{4}{3}\pi r^{3}$
$Also,\ \ mass\ (M) = volume(V) \times density(\rho)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g = \frac{G\frac{4}{3}\pi R^{3}\rho}{R^{2}}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g = \frac{4G\pi\rho R}{3}$
$Given,\ \ \ \ \ \ \ R_{1}:R_{2} = 2\ :3$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rho_{1}:\rho_{2} = \frac{3}{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{1}}{g_{2}} = \frac{\rho_{1}R_{1}}{\rho_{2}R_{2}} = \frac{3}{2} \times \frac{2}{3} = 1$