A thin horizontal movable plate P is separated from two fixed horizontal plates `P_1` and `P_2` by two highly viscous liquids of coefficient of viscosity `eta_(1)` and `eta_(2)` as shown, where `eta_2 = 4eta_(1)`. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is h, then the distance h1 of movable plate from upper fixed plate such that the movable plate can be moved with a constant velocity by applying a minimum constant horizontal force F on movable plate is (assume velocity gradient to be uniform in each liquid).

Options

A. h/4
B. h/2
C. 2h/3
D. h/3

Explanation

Let v be the velocity of the movable plate and F is equal to viscous force
`F=[eta_(1)v/(h_(1))+eta_(2)v/(h-h_(1))]A rArr (dF)/(dh_(1))=0 :. h_(1)=h/3`