A) \[\frac{4{{\pi }^{2}}{{R}^{3}}}{G}\]
B) \[\frac{4{{\pi }^{2}}{{R}^{3}}T}{G}\]
C) \[\frac{{{R}^{3}}T}{G}\]
D) \[\frac{4{{\pi }^{2}}{{R}^{3}}}{G{{T}^{2}}}\]
Correct Answer: D
Solution :
\[T=2\pi \sqrt{\frac{{{R}^{3}}}{GM}}\] \[\Rightarrow \,{{T}^{2}}=4{{\pi }^{2}}\frac{{{R}^{3}}}{GM}\Rightarrow M=\frac{4{{\pi }^{2}}{{R}^{3}}}{G{{T}^{2}}}\]
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