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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 the planet and the star is proportional to $R^{+ 5 / 2}$ , then

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detailed solution

Correct option is B

The gravitational force F ∝ 1R52 givenF=CR52−−−−−1here C is constantThe centripetal force for the planet =mRω2=mR2πT2−−−−−2Centripetal force is provided from gravitational force (1) = (2)F=CR52=mR2πT2⇒T2 ∝ R52R⇒T2 ∝ R72Therefore, the correct answer is (B)

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