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  4. The mass of the moon is (1/81) of the earth but the gravitational pull is (1/6) of the earth. It is due to the fact that

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Q. 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

Jharkhand CECEJharkhand CECE 2012

Solution:

Gravitational pull depends upon the acceleration due to gravity on that planet.
$ {{M}_{m}}=\frac{1}{81}{{M}_{e}},\,{{g}_{m}}=\frac{1}{6}{{g}_{e}} $
By the relation, $ g=\frac{GM}{{{R}^{2}}} $
$ \frac{{{R}_{e}}}{{{R}_{m}}}={{\left( \frac{{{M}_{e}}}{{{M}_{m}}}\times \frac{{{g}_{m}}}{{{g}_{e}}} \right)}^{\frac{1}{2}}}={{\left( 81\times \frac{1}{6} \right)}^{\frac{1}{2}}} $
$ \therefore $ $ {{R}_{e}}=\frac{9}{\sqrt{69}}{{R}_{m}} $