Question

According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/ \Delta Z $ is given by $ F=-\eta A\frac{\Delta v}{\Delta Z}$ , where $\eta$ is constant called coefficient of viscosity. The dimensional formula of $\eta$ is

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

Answer 1

Answer: (D)

Dimensions of force $F=[MLT^{-2}]$
Dimensions of velocity gradient $\frac{\Delta v}{\Delta Z}=\frac{[LT^{-1}]}{[L]}$
$ =[T^{-1}]$
Dimensions of area $A=[L^2]$
Given $F=-\eta A\frac{\Delta v}{\Delta Z}$
Dimensional formula for coefficient of viscocity
$\eta=\frac{F}{(A)\big(\frac{\Delta v}{\Delta Z}\big)}=\frac{[MLT^{-2}]}{[L^2][T^{-1}]}=[ML^{-1}T^{-1}]$