In a double star system, two stars of masses `m_1` and `m_2` separated by a distance `x` rotate about their centre of mass. Find the common angular velocity and Time period of revolution.

Explanation

The gravitational force between the masses provides the necessary centripetal force.
i.e. `(Gm_(1)m_(2))/(x^(2))m_(1)r_(1)omega^(2) `..1
The distance of centre of mass from `m_(1)` is
`r_(1)=(m_(2)x)/(m_(1)+m_(2))`.......2
From 1 and 2 `(Gm_(1)m_(2))/(x^(2)0=(m_(1)m_(2)x)/(m_(1)+m_(2))omega^(2)`
`omega^(2)=(G(m_(1)+m_(2)))/(x^(3))impliesomega=(sqrt(G(m_(1)+m_(2)))/(x^(3)))`
`G=(2pi)/(omega),T=2pi sqrt((x^(3))/(G(m_(1)+m_(2))))`