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» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C09_SLV_016_S01.png" width="80%"/> <br/> The gravitational force between the masses provides the necessary centripetal force <br/> `(Gm_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)m_(2))/(d) = m_(1)r_(1) omega^(2) <a href="https://interviewquestions.tuteehub.com/tag/rarr-1175461" style="font-weight:bold;" target="_blank" title="Click to know more about RARR">RARR</a> (1)` <br/> The <a href="https://interviewquestions.tuteehub.com/tag/distance-116" style="font-weight:bold;" target="_blank" title="Click to know more about DISTANCE">DISTANCE</a> of centre of mass from `m_(1)` is <br/> `r_(1) = (m_(2)d)/(m_(1)+m_(2))rarr (2)`, <br/> From (1) and (2) <br/> `(Gm_(1)m_(2))/(d^(2)) = (m_(1)m_(2)d)/(m_(1)+m_(2)).omega^(2)` <br/> (or) `omega^(2) = (G(m_(1)+m_(2)))/(d^(3))` (or) <br/> `omega = sqrt((G(m_(1) + m_(2)))/(d^(3)))`</body></html>