Question

A plate of area $2{\text{m}}^2$ is made to move horizontally with a speed of $2\text{m/s}$ by applying a horizontal tangential force over the free surface of a liquid having depth of $1\text{m}$. If the coefficient of viscosity of liquid is $0.01\text{Poise}$, find the tangential force needed to move the plate.

• A. $4\times {10}^{-3}\text{N}$
• B. $3\times {10}^{-3}\text{N}$
• C. $2\times {10}^{-3}\text{N}$
• D. $1\times {10}^{-3}\text{N}$

Answer 1

The correct option is A $4\times {10}^{-3}\text{N}$

Velocity gradient $=\frac{\Delta v}{\Delta y}=\frac{2-0}{1-0}=2{\text{s}}^{-1}$


From Newton's law of viscosity,
$|F|=\eta A\frac{\Delta v}{\Delta y}=(0.01\times {10}^{-1})\left(2\right)\left(2\right)=4\times {10}^{-3}\text{N}$