A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity omega. If two objects each mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity ...........

A thin circular ring of mass M and radius R is rotating in a horizonta

1.	A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity omega. If two objects each mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity ...........
Answer» <html><body><p>`(omegaM)/(M+2m)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/omega-585625" style="font-weight:bold;" target="_blank" title="Click to know more about OMEGA">OMEGA</a>(M+2m))/(M)`<br/>`(omegaM)/(M+m)`<br/>`(omega(M-2m))/(M+2m)` </p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C07_E05_061_S01.png" width="80%"/> <br/> According to <a href="https://interviewquestions.tuteehub.com/tag/conservation-929810" style="font-weight:bold;" target="_blank" title="Click to know more about CONSERVATION">CONSERVATION</a> of momentum, <br/> `L=L.` <br/> `therefore I_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)omega=I.omega.` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/mr-549185" style="font-weight:bold;" target="_blank" title="Click to know more about MR">MR</a>^(2)omega=(MR^(2)+2mR^(2))omega.(because I.=MR^(2)+(2m)R^(2))` <br/> `therefore Momega=(M+2m)omega.` <br/> `therefore omega.=(M)/(M+2m).omega`</body></html>