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JEE Advanced 2018Paper 2
Exam
JEE Advanced
Year
2018
Paper
Paper 2
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2018 · Paper 2 · Physics · Mechanical Properties of Fluids

Consider a thin square plate floating on a viscous liquid in a...

Consider a thin square plate floating on a viscous liquid in a large tank. The height hh 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{u}_{0} . Which of the following statements is (are) true?Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is

Options

  1. AThe resistive force of liquid on the plate is inversely proportional to hh
  2. BThe resistive force of liquid on the plate is independent of the area of the plate
  3. CThe tangential (shear) stress on the floor of the tank increases with u0{u}_{0}
  4. DThe tangential (shear) stress on the plate varies linearly with the viscosity ηη of the liquid

Correct answer

A. The resistive force of liquid on the plate is inversely proportional to hh

Step-by-step solution

Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is
Viscous force is given by F=−ηAdvdyF = - ηA\dfrac{dv}{dy} since h is very small therefore, magnitude of viscous force is given by
F=−ηA∆v∆yF = - ηA\dfrac{∆ v}{∆ y}
∴F=ηAu0h⇒F∝ηandF∝u0;F∝1h,F∝A∴ F = \dfrac{ηA{u}_{0}}{h} ⇒ F ∝ ηandF ∝ {u}_{0}; F ∝ \dfrac{1}{h}, F ∝ A
Since plate is moving with constant velocity, same force must be acting on the floor
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