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A uniform circular ring of radius R is f...

A uniform circular ring of radius `R` is first rotated about its horizontal axis with an angular velocity `omega_0` and then carefully placed on a rough horizontal surface as shown. The coefficient of friction between the surface and the rings `mu`. Time after which its angular speed is reduced to `0.5 omega_0` is

A

`(omega_(0)muR)/(2g)`

B

`(omega_(0)g)/(2muR)`

C

`(2 omega_(0)R)/(mug)`

D

`(omega_(0)R)/(2mug)`

Text Solution

Verified by Experts

The correct Answer is:
D
Taking the `tau` about `C.M.`
`mu mG R=MR^(2)alpha,mug=RalpharArralpha=(mug)/R`
`omega=omega_(0)-(mug)/Rt=(omega_(0))/2, :. T=(omega_(0)R)/(2mug)`
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Knowledge Check

  • A ring of radius R is first rotated with an angular velocity omega and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is mu . Time after which its angular speed is reduced to half is

    A
    `(omega_(0)muR)/(2g)`
    B
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    C
    `(2omega_(0)R)/(mug)`
    D
    `(omega_(0)R)/(2mug)`

  • A ring of radius R is first rotated withan angular velocity w, and then carefully placed on a rough horizontal surface. The coefficient of friction between the.surface and the ring is u. Time after which its angular speed is reduces to half is

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    B
    `(omega_(0)R)/(2mug)`
    C
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    D
    `(omega_(0)R)/(2muR)`

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    the time until rolling begins
    B
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    C
    the velocity when rolling begins
    D
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