Dimensional Analysis

Viscosity quantifies a fluid's internal resistance to flow and is defined through the tangential viscous force per unit area produced by a velocity gradient, F/A = η(dv/dx). Rearranging gives η = F / (A · dv/dx), so its dimensions follow directly from the dimensions of force, area and velocity gradient. Force has dimensions M L T^-2, area contributes L^2, and the velocity gradient dv/dx has dimensions (L T^-1)/L = T^-1. Combining these, η has dimensions (M L T^-2) / (L^2 · T^-1) = M L^-1 T^-1. The option M L T^-1 corresponds to linear momentum, not viscosity, so it is wrong. The option M L^-1 T^-2 is the dimension of pressure or stress and therefore cannot represent η. The option M L^2 T^-1 matches the dimension of angular momentum or the Planck constant and is unrelated. This treatment is identical to the NCERT derivation of the SI unit of viscosity, the poiseuille (Pa·s). A sanity check confirms consistency, since Pa·s = (N·m^-2)·s expands to M L^-1 T^-1.