A) the radius of earth is \[\frac{1}{6}\] of the moon
B) the radius of moon is \[\frac{9}{\sqrt{6}}\] of the earth
C) moon is the satellite of the earth
D) None of the above
Correct Answer: A
Solution :
Gravitational pull depends upon the acceleration due to gravity on that planet. \[{{M}_{n}}=\frac{1}{81}{{M}_{e}},\,\,{{g}_{m}}=\frac{1}{6}{{g}_{e}}\] By the relation,\[g=\frac{GM}{{{R}^{2}}}\] \[\frac{{{R}_{e}}}{{{R}_{m}}}={{\left( \frac{{{M}_{e}}}{{{M}_{m}}}\times \frac{{{g}_{m}}}{{{g}_{e}}} \right)}^{\frac{1}{2}}}={{\left( 81\times \frac{1}{6} \right)}^{\frac{1}{2}}}\]
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