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Q.

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 $R^{- 5 / 2}$

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a

$T^{2} i s p r o p o r t i n a l t o R^{3 / 7}$

b

$T^{2} i s p r o p o r t i n a l t o R^{3}$

c

$T^{2} i s p r o p o r t i n a l t o R^{7 / 2}$

d

$T^{2} i s p r o p o r t i n a l t o R^{3 / 2}$

answer is B.

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Detailed Solution

$\begin{array}{l} m R ω^{2} = \frac{G M m}{R^{5 / 2}} \\ \frac{m R 4 π^{2}}{T^{2}} = \frac{G M m}{R^{5 / 2}} \\ T^{2} \propto R^{7 / 2} \end{array}$

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