Question

What is the dimensional formula of dynamic viscosity?

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

Answer 1

Answer: (A)

$\left[m^1{L}^{-1}{T}^{-2}\right]$

Dynamic viscosity is given by:

$\mu =\tau .\frac{dy}{dc}$

here, $\tau =$ shearing stress $\frac{dy}{dc}=$ velocity gradient
$m=\left[m^1{L}^{-1}{T}^{-2}\right]\left[T^1\right]=\left[m^1{L}^{-1}{T}^{-1}\right]$ same coefficient of viscosity.