A light planet is revolving around a massive star in a circular orbit of radius \(R\) with a period of revolution \(T\). If the force of attraction between planet and star is proportional to \(\mathrm{R}^{-3 / 2}\) then choose the correct option.

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Answer & Solution

Correct Answer

(A) \(\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{F}=\frac{\mathrm{GMm}}{\mathrm{R}^{3 / 2}}=\mathrm{m} \omega^2 \mathrm{R}\)

\(\omega^2 \propto \frac{1}{\mathrm{R}^{5 / 2}} \quad \because \mathrm{T}=\frac{2 \pi}{\omega} \quad \text { so }\)

\(\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}\)

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