A) \[\frac{5}{18}{{R}_{e}}\]
B) \[\frac{1}{6}{{R}_{e}}\]
C) \[\frac{3}{18}{{R}_{e}}\]
D) \[\frac{1}{2\sqrt{3}}{{R}_{e}}\]
Correct Answer: A
Solution :
\[g=\frac{4}{3}\pi G\rho R\] \[\Rightarrow \,\,g\propto \rho R\,\Rightarrow \,\frac{{{g}_{e}}}{{{g}_{m}}}=\frac{{{\rho }_{e}}}{{{\rho }_{m}}}\times \frac{{{R}_{e}}}{{{R}_{m}}}\] \[\Rightarrow \,\,\frac{6}{1}=\frac{5}{3}\times \frac{{{R}_{e}}}{{{R}_{m}}}\,\Rightarrow \,\,{{R}_{m}}=\frac{5}{18}{{R}_{e}}\]
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