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Imagine a light planet is revolving round a very massive star in a circular orbit of radius R with a time period of revolution T. If the gravitational force of attraction between the star and planet is proportional to $R^{- n}$ , then T²is proportional to

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a

Rⁿ⁺¹

b

Rⁿ⁺²

c

R^n–1

d

R^n–2

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detailed solution

Correct option is A

$F \propto R^{- n} \Rightarrow F = {KR}^{- n}$
Gravitational Force provides necessary centripetal Force
$\begin{array}{l} {mRω}^{2} = {KR}^{- n} \Rightarrow mR \frac{4 π^{2}}{T^{2}} = {KR}^{- n} \\ \Rightarrow T^{2} = \frac{mR 4 π^{2}}{{KR}^{- n}} \Rightarrow T^{2} \propto R^{n + 1} \end{array}$

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