Question

Dimensions of coefficient of viscosity is

• A. $\left[M{T}^2\right]$
• B. $\left[M{L}^{-3}{T}^{-4}\right]$
• C. $\left[M{L}^{-1}{T}^{-2}\right]$
• D. $\left[M{L}^{-1}{T}^{-1}\right]$

Answer 1

Answer: (D)

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

Coefficient of viscosity, $\eta =\frac{F}{\frac{Adv}{dx}}$

$\left[F\right]=\left[Force\right]=ML{T}^{-2}$

$\left[A\right]=\left[Area\right]=L^2$

$\left[\frac{dv}{dx}\right]=\left[\text{Velocity gradient}\right]=\frac{L{T}^{-1}}{L}=T^{-1}$

$\therefore \left[\eta \right]=\frac{ML{T}^{-2}}{L^2{T}^{-1}}=\left[M{L}^{-1}{T}^{-1}\right]$.