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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 coefficient of viscosity varies as `eta=eta_(0)x` (x measured from centre of the disk) at the given instant the disk is floating towards right with a velocity `v` as shown, find the force required to move the disk slowly at the given instant.

A

`(2eta_(0)R^(2)v)/(T)`

B

`(8eta_(0)R^(2)v)/(T)`

C

`(pieta_(0)R^(2)v)/(T)`

D

`(16eta_(0)R^(3)v)/(T)`

Text Solution

Verified by Experts

The correct Answer is:
C
`df=etaA(dv)/(dx)`
`f=int_(0)^(R)(eta_(0)x).(2pixdx)(V)/(T)`
`f=(2)/(3).(pieta_(0)R^(3)V)/(T)`
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Knowledge Check

  • 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 .

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    A
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