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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 .

    A
    `(4piomegaetaR^(4))/(T)`
    B
    `(piomegaetaR^(4))/(2T)`
    C
    `(2piomegaetaR^(4))/(T)`
    D
    `16piomegaetaR^(4)`

  • 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))`

  • A sphere of mass M and radius R is moving on a rough fixed surface, having coefficient of friction mu . as shown in Fig. It will attain a minimum linear velocity after time v_(0)gtomega_(0)R)

    A
    `v_(0)//mug`
    B
    `omega_(0)R//mug`
    C
    `2(v_(0)-omega_(0)R)//5mug`
    D
    `2(v_(0)-omega_(0)R)//7mug`