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A thin circular ring of mass M and radiu...

A thin circular ring of mass `M` and radius `r` is rotating about its axis with a constant angular velocity `omega`. Four objects each of mass `m`, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

A

`(mOmega)/(M+43) `

B

`((M+4m)omega)/M `

C

`((M-4m)omega)/(M+4m) `

D

`(Momega)/(4m)`

Text Solution

Verified by Experts

(1) Initial angular momentum of ring = `Iomega=MR^2omega` If four object each of mass m, and kept gently to the opposite ends of two perpendicular diameters of the ring then final angular momentum = (`MR_2 + 4mR_2)omega` By the conservation of angular momentum Initial angular momentum = Final angular momentum `MR^2omega=(MR^2+4mR^2)omega.rArromega.(M/(M+4m))omega`.
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