Dimensions of the coefficient of viscosity ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The viscous force $F$ acting on a fluid layer is given by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Here,$F$ is the force,$\eta$ is t

Vedclass · Accepted Answer

$M L^{-1} T^{-1}$

Vedclass · Answer

(C) The viscous force $F$ acting on a fluid layer is given by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Here,$F$ is the force,$\eta$ is the coefficient of viscosity,$A$ is the area,and $\frac{dv}{dx}$ is the velocity gradient.Rearranging for $\eta$: $\eta = \frac{F}{A (dv/dx)}$.Substituting the dimensions: $[F] = [M L T^{-2}]$,$[A] = [L^2]$,$[dv] = [L T^{-1}]$,and $[dx] = [L]$.Thus,$[\eta] = \frac{[M L T^{-2}]}{[L^2] [L T^{-1} / L]} = \frac{[M L T^{-2}]}{[L^2] [T^{-1}]} = [M L^{-1} T^{-1}]$.Therefore,the correct option is $C$.

Dimensions of the coefficient of viscosity are

Similar Questions

The amount of solar energy received on the Earth's surface per unit area per unit time is defined as the solar constant. The dimension of the solar constant is:

Dimensions of $\varepsilon_0$ are

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$,where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$,where $A$ and $B$ are constants. The dimensions of $AB$ are

The dimensional formula of permeability of free space $\mu_0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module