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

The correct option is C Mω/(M + 2m)
Using law of conservation of angular momentum, initial angular momentum = final angular momentum,
MR2ω=(MR2+2mr2)ω
(MωM+2m)=ω, which is the new angular velocity.
Hence, the answer is (MωM+2m).

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