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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`. Two objects each of mass m, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity

A

`(omegaM)/((M+m))`

B

`(omega(M-2m))/((M+2m))`

C

`(omegaM)/((M+2m))`

D

`(omega(M+2m))/M`

Text Solution

Verified by Experts

The correct Answer is:
C
Since the objects ae placed gently, therefore no external torque is acting on the system. Therefore, angualr momentum is constant.

i.e. `I_(1)omega_(1)=I_(2)omega_(2)`
`Mr^(2)xxomega_(1)=(Mr^(2)+2mr^(2))omega_(2)`
`:. omega_(2)=(Momega)/(M+2m)`
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Knowledge Check

  • A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity omega . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity of

    A
    `(omega(M-2m))/((M + 2m))`
    B
    `(omega M)/(( M + 2m))`
    C
    `(omega M)/(( M + m))`
    D
    `(omega(M + 2m))/(M)`

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