The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that
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Gravitational pull depends upon the acceleration due to gravity on that planet.
$\mathrm{M_m} = \frac{1}{81} \mathrm{M_e}, g_m = \frac{1}{6} g_e$ $g = \frac{\mathrm{GM}}{\mathrm{R}^2} \Rightarrow \frac{\mathrm{R_e}}{\mathrm{R_m}} = \left(\frac{\mathrm{M_e}}{\mathrm{M_m}} \times \frac{g_m}{g_e}\right)^{1/2} = \left(81 \times \frac{1}{6}\right)^{1/2}$ $\therefore \mathrm{R_e} = \frac{9}{\sqrt{6}} \mathrm{R_m}$
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