Question

The dimension of dynamic viscosity is:

• A. M L$^{-1}$ T$^{-1}$
• B. M L$^{-1}$ T$^{-2}$
• C. M L$^{-2}$ T$^{-2}$
• D. M L$^{0}$ T$^{-1}$

Hint:

The dimensional formula of dynamic viscosity is derived from the ratio of force per unit area and the velocity gradient.

Answer 1

The Correct Option is A

Dynamic viscosity (\(\mu\)) is defined as the ratio of shear stress to shear rate (velocity gradient). Its dimensional formula is derived as:
\[ [\mu] = \frac{\text{Force}}{\text{Area}} \times \frac{\text{Length}}{\text{Time}}, \] where force has the dimension \(M L T^{-2}\) and area has the dimension \(L^2\). Substituting these into the equation:
\[ [\mu] = \frac{M L T^{-2}}{L^2} \times L T^{-1} = M L^{-1} T^{-1}. \] Thus, the correct dimension of dynamic viscosity is:
\[ \boxed{\text{(A) M L$^{-1}$ T$^{-1}$}}. \]