A) \[{{R}^{3/2}}\]
B) \[{{R}^{3/5}}\]
C) \[{{R}^{7/2}}\]
D) \[{{R}^{7/4}}\]
Correct Answer: D
Solution :
For revolution of planet centripetal force is provided by gravitational force of attraction \[m{{\omega }^{2}}R\propto {{R}^{-5/2}}\] \[\frac{1}{{{T}^{2}}}\propto {{R}^{-7/2}}\] \[\left[ \because \omega =\frac{2\pi }{T} \right]\] or \[{{T}^{2}}\propto {{R}^{7/2}}\] or \[T\propto {{R}^{7/4}}\]
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