In a double star system two stars of masses m_1 and m_2 seperated by a distance .d. rotates about their centre of mass. Then the common angular velocity and time period is

In a double star system two stars of masses m_1 and m_2 seperated by a

1.	In a double star system two stars of masses m_1 and m_2 seperated by a distance .d. rotates about their centre of mass. Then the common angular velocity and time period is
Answer» Solution : The GRAVITATIONAL force between the masses provides the necessary certripetal force `(Gm_1m_2)/d^2=m_1r_1omega^2 to` (1) The DISTANCE of centre of mass from `m_1` is `r_1= (m_2d)/(m_1+m_2) to` (2) From (1) and (2) `(Gm_1m_2)/d^2=(m_1m_2d)/(m_1+m_2). omega^2` `omega^2=(G(m_1+m_2))/d^3` (or) `omega=sqrt((G(m_1+m_2))/d^3)`