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In a double star system two stars of mas...

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

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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)))`
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