JEE Advanced 2018 Physics question

Consider a thin square plate floating on a viscous liquid in a large tank. The height 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 . Which of the following statements is (are) true?

(A)The resistive force of liquid on the plate is inversely proportional to 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 Correct
(D)The tangential (shear) stress on the plate varies linearly with the viscosity of the liquidCorrect

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

Solution

With a thin layer, the velocity varies linearly from at the plate to 0 at the floor, so the velocity gradient is and the shear stress everywhere in the layer is . The resistive force on the plate is

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Question ID VK-026755