In a double star system two stars of masses m_1 and m_2separated 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_2separated by a

1.	In a double star system two stars of masses m_1 and m_2separated 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 centripetal force `(Gm_1m_2)/d^2 =m_(1)r_(1)omega^2rarr(1)` The distance of centre of mass from `m_1` is `r_(1)=(m_(2)d)/(m_1+m_2)RARR(2)` From (1) and (2) `(Gm_1m_2)/d^2 =(m_1m_2d)/(m_1+m_2).omega^2` (or)`omega^2=(G(m_1+m_2))/d^3 " (or) " omega=sqrt((G(m_1+m_2))/d^3)`