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# The acceleration due to gravity on moon is only one sixth that of earth. If the earth and moon are assumed to have same densities the ratio of radii of moon and earth will be

$(a)\;\frac{1}{6} \quad (b)\;\frac{1}{(6)^{1/3}} \quad (c)\;\frac{1}{36} \quad (d)\;\frac{1}{(6)^{2/3}}$

$\large\frac{g_m}{g_e}=\frac{1}{6}$
$\qquad= \large\frac{Re^2M_m}{Rm^2M_e}$
$\qquad= \large\frac{Re^2 \Large\frac{4}{3}\pi R^3 m \rho}{R_m^2 \Large\frac{4}{3} \pi R_e^3 \rho}$
$\qquad= \large\frac{R_m}{R_e}$
$\qquad=\large\frac{1}{6}$
Hence a is the correct answer.

edited Feb 18, 2014 by meena.p