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  4. A metal plate of area text1 text0 text3 textc textm text2 rests on a layer of oil 6 mm thick. A tangential force of 10-2 textN is applied on it to move it with a constant velocity of 6 textcm texts-1. The coefficient of viscosity of the liquid is :

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Q. A metal plate of area $ \text{1}{{\text{0}}^{\text{3}}}\,\text{c}{{\text{m}}^{\text{2}}} $ rests on a layer of oil 6 mm thick. A tangential force of $ {{10}^{-2}}\,\text{N} $ is applied on it to move it with a constant velocity of $ 6\,\text{cm}{{\text{s}}^{-1}}. $ The coefficient of viscosity of the liquid is :

WBJEEWBJEE 2006

Solution:

$ \eta =\frac{F}{A(dv/dy)} $ $ \therefore $ $ \eta =\frac{{{10}^{-2}}}{({{10}^{3}}\times {{10}^{-4}})\left( \frac{6\times {{10}^{-2}}}{6\times {{10}^{-3}}} \right)}=\frac{{{10}^{-2}}\times 6\times {{10}^{-3}}}{{{10}^{-1}}\times 6\times {{10}^{-2}}} $ $ ={{10}^{-2}}N-s-{{m}^{2}}=0.1 $ Poise