A) \[{{R}^{3}}\]
B) \[{{R}^{7/2}}\]
C) \[{{R}^{5/2}}\]
D) \[{{R}^{3/2}}\]
Correct Answer: B
Solution :
Gravitational force is equal to centripetal force \[\frac{GMm}{{{R}^{5/2}}}=\frac{m{{\upsilon }^{2}}}{R}\] \[{{\upsilon }^{2}}=\frac{GM}{{{R}^{3/2}}}\] Time period \[{{T}^{2}}=\frac{4{{\pi }^{2}}{{R}^{2}}}{{{\upsilon }^{2}}}=\frac{4{{\pi }^{2}}{{R}^{2}}}{GM}\times {{R}^{3/2}}\] \[=\frac{4{{\pi }^{2}}{{R}^{7/2}}}{GM}\] \[{{T}^{2}}\propto {{R}^{7/2}}\]
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