JEE Mains · Physics · STD 11 - 7. gravitation
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.
- A \(\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}\)
- B \(T^2 \propto R^{7 / 2}\)
- C \(T^2 \propto R^{3 / 2}\)
- D \(T^2 \propto R^3\)
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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