Question

The dimensional formula of coefficient of viscosity is

• A. $\left[ML{T}^{-1}\right]$
• B. $\left[M^{-1}{L}^2{T}^{-2}\right]$
• C. $\left[M{L}^{-1}{T}^{-1}\right]$
• D. none

Answer 1

Answer: (C)

$\left[M{L}^{-1}{T}^{-1}\right]$

Coefficient of viscosity is given by $\eta =\frac{F}{A}\frac{dz}{dv}$
Dimension of force $F=\left[ML{T}^{-2}\right]$
Dimension of Area $A=\left[L^2\right]$
Dimension of velocity gradient $\frac{dv}{dz}=\left[T^{-1}\right]$
Thus dimension of coefficient of viscosity $\eta =\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]\left[T^{-1}\right]}=\left[M{L}^{-1}{T}^{-1}\right]$