# 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

a. $$2\pi = \sqrt{\frac{d^{3}}{3Gm}}$$

b. $$\frac{1}{2\pi} = \sqrt{\frac{3Gm}{d^{3}}}$$

c. $$\frac{1}{2\pi} = \sqrt{\frac{d^{3}}{3Gm}}$$

d. $$2\pi = \sqrt{\frac{3Gm}{d^{3}}}$$

⇒ G(m)(2m) / d2 = mω2 × 2d / 3

⇒ 2Gm / d2 = ω2 × 2d / 3

⇒ ω2 = 3Gm / d3

⇒ $$\omega = \sqrt{\frac{3Gm}{d^{^{3}}}}$$

We know that, ω = 2π / T so T = 2π / ω

⇒ $$T = \frac{2\pi }{\sqrt{\frac{3Gm}{d^{3}}}} \Rightarrow T = 2\pi\sqrt{\frac{d^{3}}{3Gm}}$$