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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.

The torque required to rotate the disk at a constant angular velocity `Omega` given the viscosity is uniformly `eta`.

A

`(4piomegaetaR^(4))/(T)`

B

`(piomegaetaR^(4))/(2T)`

C

`(2piomegaetaR^(4))/(T)`

D

`16piomegaetaR^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B

`dF=eta(dA)(dv)/(dx)=eta(2pir)dr.(romega)/(T)` on integrating
`int_(0)^(tau)dtau=int_(0)^(R).r=int_(0)^(R)(eta2pir^(3)omegadr)/(T),tau=(piomegaetaR^(4))/(2T)`
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