Question

A large wooden plate of area $10m^2$ floating on the surface of a river is made to move horizontally with a speed of $2m/s$ by applying a tangential force. River is $1m$ deep and the water in contact with the bed is stationary. Then choose correct statement. (coefficient of viscosity of water $={10}^{-3}N-s/m^2)$

• A. velocity gradient is $2s^{-1}$
• B. velocity gradient is $-1s^{-1}$
• C. force required to keep the plate moving with constant speed is $0.02N$
• D. force required to keep the plate moving with constant speed is $0.01N$

Answer 1

Answer: (A), (C)

The correct options are
A velocity gradient is $2s^{-1}$
C force required to keep the plate moving with constant speed is $0.02N$

Velocity gradient$=\frac{\Delta v}{\Delta h}=\frac{2m/s}{1m}=2s^{-1}$
$F=\eta A\frac{\Delta v}{\Delta h}$
$=\left({10}^{-3}\right)\left(10\right)\left(2\right)$
$=0.02$ N