JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Fluid Mechanics

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?

(A)The resistive force of liquid on the plate is inversely proportional to $h$ ✓ Correct
(B)The resistive force of liquid on the plate is independent of the area of the plate
(C)The tangential (shear) stress on the floor of the tank increases with $u_{0}$ ✓ Correct
(D)The tangential (shear) stress on the plate varies linearly with the viscosity $η$ of the liquid✓ Correct

Answer: (A), (C), (D)

Solution

The viscous force on a plate moving through a liquid is given by

F_{v} = \frac{η A u _{0}}{h}

, where

A

is the area of the plate. This shows

F_{v} \propto \frac{1}{h}

(A is correct) and

F_{v} \propto A

(B is incorrect). The shear stress is

\frac{F}{A} = \frac{η u _{0}}{h}

, which is proportional to both

η

(D is correct) and

u_{0}

(C is correct).

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · One or more correct options