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» `(omegaM)/(M+2m)` `(OMEGA(M+2m))/(M)` `(omegaM)/(M+m)` `(omega(M-2m))/(M+2m)` Solution : According to CONSERVATION of momentum, `L=L.` `therefore I_(1)omega=I.omega.` `MR^(2)omega=(MR^(2)+2mR^(2))omega.(because I.=MR^(2)+(2m)R^(2))` `therefore Momega=(M+2m)omega.` `therefore omega.=(M)/(M+2m).omega`