Physics - Unit & Dimension Question with Solution | TestHub

Viscous force is given by $F=\eta A\left(\frac{dv}{dt}\right)$, here, $A$ is area and $\frac{dv}{dt}$ is velocity gradient.

Thus, $\eta =\frac{F}{A\left({\displaystyle \frac{dv}{dt}}\right)}$.

Now,  $Pt=\frac{F}{A}t=\eta \left(\frac{dv}{dt}\right)t$

Then, $\left[Pt\right]=M{L}^{-1}{T}^{-1}=\left[\eta \right]$

Thus, assertion is true but reason is false.