Question

According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\frac{\Delta v}{\Delta z}$ is given by $F=-\eta a\frac{dv}{dz}$, where $\eta$ is constant called

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

Answer 1

The correct option is D $\left[M^{}{L}^{-1}{T}^{-1}\right]$

$\begin{array}{c}F=-\eta A\frac{\Delta v}{\Delta t}\\ \eta =\frac{F}{A\left(\frac{\Delta v}{\Delta t}\right)}\\ \left[\eta \right]=\frac{\left[F\right]}{\left[A\right]\left[\frac{\Delta v}{\Delta t}\right]}=\frac{\left(M^1{L}^1{T}^{-2}\right)}{\left[L^2\right]\left[T^{-1}\right]}\\ \eta =\left[M^1{L}^{-1}{T}^{-1}\right]\end{array}$