Q 11-07-140JEE MainJEE Main 2021 (24 Feb, Shift 1)Easy
Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is
Answer: (A) $2\pi\sqrt{\frac{d^3}{3Gm}}$
The star of mass $m$ moves in a circle of radius $r = \dfrac{2m}{3m}d = \dfrac{2d}{3}$ about the centre of mass. Gravity provides its centripetal force:
$$\frac{G(m)(2m)}{d^2} = m\omega^2\cdot\frac{2d}{3} \;\Rightarrow\; \omega^2 = \frac{3Gm}{d^3}$$
$$T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{d^3}{3Gm}}$$
Solution by Sreeraj P, M.Sc Physics