Question

The viscous force on a small sphere of radius $R$ moving in a fluid varies as $(\mathrm{A}) \propto R^{2}$ (B) $\propto R$ (C) $\propto(1 / R)$ $(\mathrm{D}) \propto(1 / R)^{2}$

Name: Problem 41, Chapter 8: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T00:39:12-08:00
Duration: 1 min 7 s
Channel: Mahipal Kumawat
Description: The viscous force on a small sphere of radius R moving in a fluid varies as (A) ∝R^2 (B) ∝R (C) ∝(1 / R) (D) ∝(1 / R)^2

   The viscous force on a small sphere of radius $R$ moving in a fluid varies as
$(\mathrm{A}) \propto R^{2}$
(B) $\propto R$
(C) $\propto(1 / R)$
$(\mathrm{D}) \propto(1 / R)^{2}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 8, Problem 41

Instant Answer

Solved by Expert Mahipal Kumawat

10/06/2021

Step 1

According to Stokes' law, the viscous force (F) is given by the formula: \[ F = 6\pi\eta Rv \] where: - $ \eta $ is the dynamic viscosity of the fluid, - $ R $ is the radius of the sphere, and - $ v $ is the terminal velocity of the sphere. Show more…

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The viscous force on a small sphere of radius $R$ moving in a fluid varies as $(\mathrm{A}) \propto R^{2}$ (B) $\propto R$ (C) $\propto(1 / R)$ $(\mathrm{D}) \propto(1 / R)^{2}$

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Key Concepts

Stokes' Law

Stokes' Law defines the viscous drag force experienced by small spherical objects moving in a viscous fluid at low Reynolds numbers. It establishes that the drag force is directly proportional to the radius of the sphere, the fluid's viscosity, and the object's velocity. This principle is crucial in fluid mechanics for predicting and understanding the behavior of particles in fluids.

Viscosity

Viscosity is a property of fluids that quantifies their resistance to flow and deformation. It is a key factor in determining the magnitude of the drag force acting on objects moving through the fluid, as higher viscosity leads to larger internal friction and, consequently, a higher force opposing motion.

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