Question

A large plastic plate of area $40{\text{m}}^2$ is floating on the surface of a river. Determine the tangential force that should be applied on the plastic plate to move the plate at $4\text{m/s}$ on the surface of the river. The depth of the river is $2\text{m}$ and coefficient of viscosity of water is ${10}^{-2}$ poise.

• A. $0.16\text{N}$
• B. $1.6\text{N}$
• C. $0.08\text{N}$
• D. $0.2\text{N}$

Answer 1

The correct option is C $0.08\text{N}$

Assuming that the water in contact with the river bed is stationary, velocity gradient $\frac{dv}{dx}=\frac{4-0}{2}=2{\text{s}}^{-1}$
Now, coefficient of viscosity $\left(\eta \right)=\left|\frac{\frac{F}{A}}{\frac{dv}{dx}}\right|$
From the data given in the question,
$\eta ={10}^{-3}=\frac{F}{40\times 2}$
$[\because 1\text{poise}=0.1\text{Pa s}]$
$\Rightarrow F=0.08\text{N}$
Hence, option (a) is the correct answer.