Imagine a light planet revolving around a very massive star in a circular orbit

Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to

R^{\frac{- 5}{2}}

, then

T^{2}

is proportional to

Options:

A . R3

B . R72

C . R52

D . R32

Answer: Option B
:
B
For revolution of planet centripetal force is provided by gravitational force of attraction

m ω^{2} R \propto R^{\frac{- 5}{2}} \Rightarrow \frac{1}{T^{2}} \propto R^{\frac{7}{2}}

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