Question

Which one of the following represents the correct dimensions of the coefficient of viscosity? (A) $\left[M L^{-1} T^{-2}\right]$ (B) $\left[M L T^{-1}\right]$ (C) $\left[M L^{-1} T^{-1}\right]$ (D) $\left[M L^{-2} T^{-2}\right]$

Name: Problem 106, Chapter 1: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-10T05:42:29-08:00
Duration: 1 min 14 s
Channel: Akshaya Rs
Description: Which one of the following represents the correct dimensions of the coefficient of viscosity? (A) [M L^-1 T^-2] (B) [M L T^-1] (C) [M L^-1 T^-1] (D) [M L^-2 T^-2]

   Which one of the following represents the correct dimensions of the coefficient of viscosity? 
(A) $\left[M L^{-1} T^{-2}\right]$
(B) $\left[M L T^{-1}\right]$
(C) $\left[M L^{-1} T^{-1}\right]$
(D) $\left[M L^{-2} T^{-2}\right]$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 1, Problem 106

Instant Answer

Solved by Expert Akshaya Rs

10/10/2021

Step 1

Step 1: We start by recalling the Stokes' law which gives the expression for the drag force as $F = 6\pi \eta rv$, where $\eta$ is the coefficient of viscosity, $r$ is the radius of the object and $v$ is the velocity of the object. Show more…

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Which one of the following represents the correct dimensions of the coefficient of viscosity? (A) $\left[M L^{-1} T^{-2}\right]$ (B) $\left[M L T^{-1}\right]$ (C) $\left[M L^{-1} T^{-1}\right]$ (D) $\left[M L^{-2} T^{-2}\right]$

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Key Concepts

Coefficient of Viscosity

The coefficient of viscosity quantifies a fluid's internal resistance to flow or deformation. In fluid dynamics, it is used as a proportionality constant in Newton's law of viscosity, which relates the shear stress between adjacent fluid layers to the velocity gradient perpendicular to the flow.

Dimensional Analysis

Dimensional analysis is a method used to check the consistency of equations and to derive the units of physical quantities by expressing them in terms of fundamental dimensions such as mass, length, and time. This technique ensures that physical equations are dimensionally valid.

Physical Quantity Dimensions

Fundamental physical quantities like mass, length, and time form the basis of dimensional analysis. Through combining these basic dimensions, one can express the dimensions of more complex quantities, such as the coefficient of viscosity, ensuring that derived expressions remain consistent and meaningful.

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