Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the…

1. The resistive force of liquid on the plate is inversely proportional to $h$
2. The resistive force of liquid on the plate is independent of the area of the plate
3. The tangential (shear) stress on the floor of the tank increases with $u_0$
4. The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

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
$F=-\eta A\frac{∆v}{∆y}$
$\therefore F=\frac{\eta A{u}_0}{h}\Rightarrow F\propto \eta \mathrm{a}\mathrm{n}\mathrm{d} F\propto u_0;F\propto \frac{1}{h},F\propto A$
Since plate is moving with constant velocity, same force must be acting on the floor

Asked in: JEE Advanced 2018 (Paper 2)

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