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A thin square plate floats on a viscous liquid in a large tank. The depth of the liquid h is smaller than the width of the tank. The plate is pulled horizontally at a constant velocity u0. Which of the following statements are correct?

1. (A) The resistive force of the liquid on the plate is inversely proportional to h.
2. (B) The resistive force of the liquid on the plate is independent of the area of the plate.
3. (C) The tangential (shear) stress on the floor of the tank increases with u0.
4. (D) The tangential (shear) stress on the plate varies linearly with the viscosity eta of the liquid.

Correct answer: (A) The resistive force of the liquid on the plate is inversely proportional to h.

Solution

With linear velocity profile, tau = eta*u0/h. Resistive force F = tau*A = eta*u0*A/h, so F is inversely proportional to h (A true), proportional to area A (B false), tau increases with u0 (C true), and tau is linear in eta (D true). Correct statements are A, C, and D.

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