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Consider a disk of mass m, radius R lyin...


Consider a disk of mass `m`, radius `R` lying on a liquid layer of thickness T and coefficient of viscosity `eta` as shown in the fig.
A disc rotating with angularvelocity `omega` is placed on a viscous liquid of thickness T. Find the angle rotated by the disc before it comes to rest. (viscosity`=eta`, mass of disc `=M`, radius of disc `=R`)

A

`(4omega_(0)TM)/(etapiR^(2))`

B

`(2omega_(0)TM)/(etapiR^(2))`

C

`(omega_(0)TM)/(etapiR^(2))`

D

`(omega_(0)TM)/(2etapiR^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`tau=(piomegaetaR^(4))/(2T)=Ialpha=(MR^(2))/(2)alpha` and `alpha=omega.(domega)/(dtheta)`
`becausetheta=(omegaTM)/(etapiR^(2))`
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