JEE Advanced2018PhysicsMechanical Properties of FluidsActual
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?
Options
- AThe resistive force of liquid on the plate is inversely proportional to h
- BThe resistive force of liquid on the plate is independent of the area of the plate
- CThe tangential (shear) stress on the floor of the tank increases with u 0
- DThe tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid
Correct answer
A. The resistive force of liquid on the plate is inversely proportional to h
Step-by-step solution
Viscous force is given by F = - η A d v d y since h is very small therefore, magnitude of viscous force is given by F = - η A ∆ v ∆ y ∴ F = η A u 0 h ⇒ F ∝ η a n d F ∝ u 0 ; F ∝ 1 h , F ∝ A Since plate is moving with constant velocity, same force must be acting on the floor