JEE PYQ: Gravitation Question 10
Question 10 - 2021 (24 Feb Shift 1)
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:
(1) $2\pi\sqrt{\frac{d^3}{3Gm}}$
(2) $\frac{1}{2\pi}\sqrt{\frac{3Gm}{d^3}}$
(3) $\frac{1}{2\pi}\sqrt{\frac{d^3}{3Gm}}$
(4) $2\pi\sqrt{\frac{3Gm}{d^3}}$
Show Answer
Answer: (1)
Solution
Centre of mass divides the distance in ratio $2:1$. For mass $m$: $\frac{Gm(2m)}{d^2} = m\omega^2 \times \frac{2d}{3}$. $\omega^2 = \frac{3Gm}{d^3}$. $T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{d^3}{3Gm}}$.
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