JEE Advanced 2018 · Paper 2 · Physics Q2

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PhysicsMultiple correct+4 / -2Question 2 of 54

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?

The resistive force of liquid on the plate is inversely proportional to

h

The resistive force of liquid on the plate is independent of the area of the plate

The tangential (shear) stress on the floor of the tank increases with

u_0

The tangential (shear) stress on the plate varies linearly with the viscosity

\eta

of the liquid

Answer and worked solution

Official answer: A, C, D

The liquid layer is thin ( $h\ll$ width), so the velocity varies linearly from $u_0$ at the plate to 0 at the floor. The shear stress is the same throughout the layer:
$\tau=\eta\frac{u_0}h,\qquad F=\tau A=\frac{\eta Au_0}h.$

(A) $F\propto1/h$ . True.
(B) $F\propto A$ . False.
(C) The floor feels the same stress, $\eta u_0/h$ , which increases with $u_0$ . True.
(D) The stress is proportional to $\eta$ . True.

(A), (C), (D)

Topics:Viscosity and Stokes' law

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JEE Advanced 2018 · Paper 2, Physics question 2