Q 11-07-057JEE MainJEE Main 2024 (1 Feb, Shift 2)Medium
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 the planet and the star is proportional to $R^{-3/2}$, then choose the correct option.
Answer: (A) $T^2 \propto R^{5/2}$
The attraction provides the centripetal force:
$$m\omega^2R = kR^{-3/2} \Rightarrow \omega^2 \propto R^{-5/2}$$
Since $T = \dfrac{2\pi}{\omega}$, $T^2 \propto R^{5/2}$.
Solution by Sreeraj P, M.Sc Physics