$\large\frac{g_m}{g_e}=\frac{1}{6}$

$\qquad= \large\frac{Re^2M_m}{Rm^2M_e}$

$\qquad= \large\frac{Re^2 \Large\frac{4}{3}\pi R^3 m \rho}{R_m^2 \Large\frac{4}{3} \pi R_e^3 \rho}$

$\qquad= \large\frac{R_m}{R_e}$

$\qquad=\large\frac{1}{6}$

Hence a is the correct answer.