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