Question

A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 Poise, distance between the plates in metre is:

• A. 0.1
• B. 0.05
• C. 0.005
• D. 0.0005

Answer 1

Answer: (D)

Given: Coefficient of viscosity $\eta =0.01$ poise $={10}^{-2}poise={10}^{-3}kg/ms$ Viscous force $=0.002N=2\times {10}^{-3}N$ $(\because 1poise=\frac{1}{10}kg/ms)$ Length of square plate =0.1 m Area of square plate $A=0.1\times 0.1={10}^{-2}{m}^2$ Velocity $=0.1m/s={10}^{-1}m/s$ From relation, the viscous force is given by $F=\eta A\frac{dv}{dx}$ or $dx=\frac{\eta Av}{F}$ $=\frac{{10}^{-3}\times {10}^{-2}\times {10}^{-1}}{2\times {10}^{-3}}=\frac{{10}^{-3}}{2}$ $=0.5\times {10}^{-3}=0.0005m$