A plate of area `2m^(2)` is made to move horizontally with a speed of `2m//s` by applying a horizontal tangential force over the free surface of a liquid. If the depth of the liquid is 1m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid is `0.01` poise. Find the tangential force needed to move the plate.

Options

A. `4xx10^(-3) N`
B. `14xx10^2 N`
C. `4xx10^(-2) N`
D. 4 N

Answer

A

Explanation

Velocity gradient `=(2-0)/(1-0)=2s^(-1)`

from newton's law of viscous force,
`|F|=etaA(Deltav)/(Deltay)=(0.01xx10^(-1))(2)(2)`
`=4xx10^(-3)N`
So , to keep the plate moving a force of `4xx10^(-3)N` must be applied.