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Question:

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 u0. Which of the following statements is (are) true?

The tangential (shear) stress on the floor of the tank increases with u0.

The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid.

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

Solution:

Viscous force is given by F = −ηA(dv/dy) since h is very small, so magnitude of viscous force is given by F = ηAΔv/Δy ∴ F = ηAu0/h (Because v = u0 and y = height of fluid (h)) ⇒ F ∝ η, F ∝ u0; F ∝ 1/h, F ∝ A Since plate is moving with constant velocity, same force must be acting on the floor. So Option (A), (C) and (D) are correct