In a double star system two stars of masses m_(1) and m_(2) separated 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) separated

1.	In a double star system two stars of masses m_(1) and m_(2) separated 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_(1)m_(2))/(d) = m_(1)r_(1) omega^(2) RARR (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_(1)m_(2))/(d^(2)) = (m_(1)m_(2)d)/(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)))`