Physics · Mechanical Properties of Matter

JEE Advanced 2018 — Paper 2 — Question 2

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?

Option A:
The resistive force of liquid on the plate is inversely proportional to $h$
Correct
Option B:
The resistive force of liquid on the plate is independent of the area of the plate
Option C:
The tangential (shear) stress on the floor of the tank increases with $u_{0}$
Correct
Option D:
The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid
Correct

Answer: A, C, D

Step-by-step solution

$\mathrm{F}_{\mathrm{v}}=\left|\frac{\eta \mathrm{Au}_{0}}{\mathrm{~h}}\right|$

$\mathrm{F}_{\mathrm{v}} \propto \frac{1}{\mathrm{~h}}, \mathrm{~F}_{\mathrm{v}} \propto \mathrm{A}$ and

Shear Stress $=\frac{F}{A} \propto \eta$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2018
Paper: Paper 2
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity

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