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A ring of radius R is first rotated with...

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

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Taking `tau` about CM

`mumgR=MR^(2) alpha`
`mug=Ralpha`
`alpha=(mug)/R`
`omega=omega_(0)=(mug)/Rf=(omega_(0))/2`
`(omega_(0))/2=(mug)/Rfimpliesf=(omega_(0)R)/(2mug)`
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Knowledge Check

  • 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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