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Question

# A thin circular ring of 'M' and radius 'R' is rotating about its axis with a constant angular velocity ω. 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.

A
Mω(M+m)
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B
2mMω(M+2m)
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C
Mω(M+2m)
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D
(M+2m)ωM
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Solution

## The correct option is C Mω(M+2m)Let I be MOI of ring initially and w be its angular velocity Let them change to I' and w'I=mR2I=MR2+2mR2=(M+2m)R2Li=Iωangularmomentumisconserved∴Iω=I′ω′⇒ω′=II′ω=M(M+2m)ω

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