1. Tardigrade
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  4. 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:

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Q. 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:

EAMCETEAMCET 2003

Solution:

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 \,1\,poise\,=\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}}=0.0005\,m $