Browse Questions

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

$(a)\;\frac{1}{6} \quad (b)\;\frac{1}{(6)^{1/3}} \quad (c)\;\frac{1}{36} \quad (d)\;\frac{1}{(6)^{2/3}}$
Can you answer this question?

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

answered Aug 29, 2013 by
edited Feb 18, 2014 by meena.p