JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Fluid Mechanics

Assertion A (True): The dimension of pressure $P$ is $[M{L}^{-1}{T}^{-2}]$ and time $t$ is $[T]$. Therefore, $Pt$ has dimension $[M{L}^{-1}{T}^{-1}]$. The coefficient of viscosity $\eta =\frac{F}{Av/d}$ where $A$ is area and $v/d$ is velocity gradient. This gives dimension $\frac{[ML{T}^{-2}]}{[L^2][T^{-1}]}=[M{L}^{-1}{T}^{-1}]$. So Assertion A is correct.

Reason R (False): The formula given is incomplete. Coefficient of viscosity is $\eta =\frac{F\cdot d}{A\cdot v}$ or equivalently $\eta =\frac{F}{A\times (\text{velocity gradient})}$, not just $\frac{\text{Force}}{\text{Velocity gradient}}$. The area term is missing, making Reason R incorrect.

Therefore, A is true but R is false.