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Imagine a light planet in revolving round a very massive star in a circular orbit of radius R with a time period of revolution T. If the gravitation force of attraction between the star and planet is proportional to R^-n, then T² is proportional to

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Rⁿ⁺¹

Rⁿ⁺²

R^n-1

R^n-2

answer is A.

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Detailed Solution

$\frac{- GMm}{R^{n}} = mR ω^{2} = mR \frac{4 π^{2}}{T^{2}} T^{2} = \frac{4 π^{2} R^{n + 1}}{G M} ∴ T^{2} \propto R^{n + 1}$

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