Discussion
The basic dimensions, i.e., mass, length, and time are represented by M, L, and T, respectively. The correct dimension of dynamic viscosity is
Answer: C
The dimension of dynamic viscosity is \(ML^{-1}T^{-1}\).
From Newton's law of viscosity, \(\tau = \mu\,du/dy\):
\[ \begin{aligned} [\tau] &= \frac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2} \\ [du/dy] &= T^{-1} \\ [\mu] &= ML^{-1}T^{-1} \end{aligned} \]
This matches the SI unit Pa.s, which is kg.m-1.s-1. \(MLT^{-2}\) is the dimension of force, and \(L^{2}T^{-1}\) is kinematic viscosity, \(\nu = \mu/\rho\), which has no mass dimension. \(L^{-2}T^{2}\) corresponds to no standard fluid property.
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