Question

A square plate of $1\text{m}$ side moves parallel to a second plate with velocity $4\text{m/s}$. A thin layer of water exist between plates. If the viscous force is $2\text{N}$ and the coefficient of viscosity is $0.01\text{Poise}$, then find the distance between the plates.

• A. $4\text{mm}$
• B. $3\text{mm}$
• C. $2\text{mm}$
• D. $1\text{mm}$

Answer 1

The correct option is C $2\text{mm}$

Force, $F=2\text{N}$
Coefficient of viscosity, $\eta =0.01\text{Poise}=0.01\times {10}^{-1}\text{Pa.s}$
Area, $A=1\times 1=1{\text{m}}^2$
We know that, Viscous force $F_v=\frac{\eta Av}{d}\Rightarrow d=\frac{\eta Av}{F}=\frac{0.01\times {10}^{-1}\times 1^2\times 4}{2}=2\times {10}^{-3}\text{m}=2\text{mm}$