A) \[\frac{\omega \,(M-2m)}{(M+2m)}\]
B) \[\frac{\omega M}{(M+2m)}\]
C) \[\frac{\omega M}{(M+m)}\]
D) \[\frac{\omega (M+2m)}{M}\]
Correct Answer: B
Solution :
Given: Mass of ring = M; Radius of ring = r; Initial angular velocity \[({{\omega }_{1}})=\omega ;\] Mass added with the ring = 2 m and final angular velocity\[({{\omega }_{2}}).\] We know from the conservation of angular moment\[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] or \[M{{r}^{2}}\omega =(M+2m)\,{{r}^{2}}\omega \]or\[\omega =\frac{\omega M}{(M+2m)}\]
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