Question

A metal plate $0.02m^2$ in area is lying on a liquid layer of thickness ${10}^{-3}m$ and coefficient of viscosity $140poise$. Calculate the horizontal force needed to move the plate with a speed of $0.040m/s$.

• A. $11.2N$
• B. $22.4N$
• C. $5.6N$
• D. $44.8N$

Answer 1

The correct option is A $11.2N$

Area of the plate, $A=0.02m^2$
Thickness, $△x={10}^{-3}m$
$△v=0.04m/s$
$△x$ is the distance of the free surface with respect to the fixed surface.
Velocity gradient, $\frac{△v}{△x}=\frac{0.04}{{10}^{-3}}=40s^{-1}$
Coefficient of viscosity,
$\eta =14kg$-$m^{-1}{s}^{-1}$

Let $F$ be the required force.
Then,
$F=\eta A\frac{△v}{△x}=11.2N$