Question

# A thin circular ring of mass $$M$$ and radius $$R$$ is rotating about its axis with a constant angular velocity. Two objects, each of mass $$m$$ are attached gently to the opposite ends of the diameter of the ring. The wheel now rotates with an angular velocity of :

A
Mω/(M + m)
B
(M+2m)/(Mω +2m)
C
Mω/(M + 2m)
D
(M + 2m)/Mω

Solution

## The correct option is C M$$\omega$$/(M + 2m)Using law of conservation of angular momentum,  initial angular momentum $$=$$ final angular momentum,$$\Rightarrow MR^2\omega =\left(MR^2+2mr^2\right)\omega '$$$$\Rightarrow \left( \dfrac { M\omega }{ M+2m } \right) =\omega ',$$ which is the new angular velocity. Hence, the answer is $$\left( \dfrac { M\omega }{ M+2m } \right).$$Physics

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