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Q.

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?

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a

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

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 u0

d

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

answer is A.

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Detailed Solution

viscous force is given by F=−ηAdvdy since h is very small therefore; magnitude of viscous force is given by ∴ F∝1h∴option 1 is correct F∝A ∴option 2 is incorrect ∴ F=ηAu0h⇒F∝η ∴Option 4 is correct & F∝u0 ∴Option 3 is correct

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