A planet revolving around |CoordinationCompoundsJEEMAIN2023

JEE MAIN 2024

01-02-2024 S2

Question

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 :

Select the correct option:

$T^2 \propto R^{5 / 2}$

$\mathrm{T}^2 \propto \mathrm{R}^{7 / 2}$

$T^2 \propto R^{3 / 2}$

$T^2 \propto R^3$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \mathrm{F}=\frac{\mathrm{GMm}}{\mathrm{R}^{3 / 2}}=\mathrm{m} \omega^2 \mathrm{R} \\ & \omega^2 \propto \frac{1}{\mathrm{R}^{5 / 2}} \because \mathrm{~T}=\frac{2 \pi}{\omega} \text { so } \\ & \mathrm{T}^2 \propto \mathrm{R}^{5 / 2}\end{aligned}$

Question Tags

JEE Main

Physics

Hard

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