Q. Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?
Solution:
Viscous force is given by $F = - \eta A \frac{dv}{dy}$ since h is very small therefore, magnitude of viscous force is given by
$F = \eta A \frac{\Delta v}{\Delta y}$
$\therefore \, \, F = \frac{\eta A u_0}{h} \, \Rightarrow F \propto \eta \, \& \, F \propto u_0 ; F \propto \frac{1}{h} , F \propto A $
Since plate is moving with constant velocity, same force must be acting on the floor.
