A) \[4{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\]
B) \[8{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\]
C) \[12{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\]
D) \[16{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\]
Correct Answer: A
Solution :
\[m{{\omega }^{2}}R=\frac{GMm}{{{R}^{2}}}\,\Rightarrow \,{{\left( \frac{2\pi }{T} \right)}^{2}}R=\frac{GM}{{{R}^{2}}}\]\[\Rightarrow \,M=\frac{4{{\pi }^{2}}{{R}^{3}}}{G{{T}^{2}}}\]
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