Q 11-07-043JEE MainJEE Main 2026 (2 Apr, Shift 1)Easy
A planet $(P_1)$ is moving around the star of mass $2M$ in the orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in a orbit of radius $2R$. Ratio of time periods of revolution of $P_2$ and $P_1$ is ______.
Answer: (B) $2$
For a circular orbit, $T=2\pi\sqrt{\dfrac{r^3}{GM}}$, so $T\propto\sqrt{\dfrac{r^3}{M}}$.
$$\frac{T_2}{T_1}=\sqrt{\frac{(2R)^3/(4M)}{R^3/(2M)}}=\sqrt{\frac{8}{2}}=2$$
Solution by Sreeraj P, M.Sc Physics