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)`

Consider a disk of mass `m`, radius `R` lying on a liquid layer of th

1.	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)`
Answer» Correct Answer - 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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