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A ring of radius R is first rotated with an angular velocity $ω_{0}$ and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is $μ$ . Time after which its angular speed is reduced to half is

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ω0μR2g

ω0g2μR

2ω0Rμg

ω0R2μg

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detailed solution

Correct option is D

Taking τ about CMμmgR=MR2αμg=Rαα=μgRω=ω0−μgRt=ω02⇒ω02=μgRt⇒t=ω0R2μg

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A ring of radius R is first rotated with an angular velocity ω0 and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is μ. Time after which its angular speed is reduced to half is

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A ring of radius R is first rotated with an angular velocity $ω_{0}$ and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is $μ$ . Time after which its angular speed is reduced to half is