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A space 2.5 cm wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5 m^{2}$ just midway the surface at a speed of $0.5 m s^{- 1}$ is 1N.Find the coefficient of viscosity of oil (in $\times 10^{- 3} k g - m^{- 1} s^{- 1}$ )

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answer is 25.

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Detailed Solution

Velocity gradient $= \frac{Δ v}{Δ y} = \frac{0.5 - 0}{1.25 \times 10^{- 2}} = 40 s^{- 1}$

$F = 2 [η A \frac{Δ v}{Δ y}] \Rightarrow 1 = 2 \times η \times 0.5 \times 40 η = \frac{1}{40} k g - m^{- 1} s^{- 1} o r η = 0.25 \times 10^{- 1} = 25 \times 10^{- 3} k g m^{- 1} s^{- 1}$

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