Question

A thin circular ring of mass $ M $ and radius $ r $ is rotating about its axis with constant angular velocity $ \omega $ . Two objects each of mass $ m $ , are placed gently at the opposite ends of diameter of the ring. The ring now rotates with an angular velocity

• A. $ \omega M/(M+m) $
• B. $ \omega M/(M+2m) $
• C. $ \omega (M-2m)/(m+2M) $
• D. $ \omega (M+2m)/M $

Answer 1

The Correct Option is B

As on torque is acting on the system, so from law of conservation of angular momentum, Initial angular momentum = final angular momentum . i.e., $M r^{2} \omega=(M+2 m) r^{2} \omega$ $\Rightarrow \omega'=\frac{M \omega}{(M+2 m)}$