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Q.

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 surfaces at a speed of 0.5 m/sec is 1 N. The coefficient of viscosity in kg - s/ $m^{2}$ is:

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a

$1 \times 10^{- 2}$

b

$5 \times 10^{- 2}$

c

$2.5 \times 10^{- 2}$

d

$7.5 \times 10^{- 2}$

answer is B.

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Detailed Solution

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Velocity gradient = $\frac{0.5}{\frac{2.5}{2} \times 10^{- 2}}$
as force on the plate due to viscosity is from upper as well as lower portion of the oil, equal from each part,
Then, $F = 2ηA \frac{dv}{dz} = 2 \times η \times (0.5) \frac{0.5}{1.25 \times 10^{- 2}}$

$\Rightarrow η = 2.5 \times 10^{- 2} kg - \sec / m^{2}$

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