MCQ
A space $2.5\ cm$ wide between two large plane surfaces is filled with oil. Force required to drag 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 :
  • A
    $5\,\, \times \,{10^{ - 2}}$
  • $2.5\,\, \times \,\,{10^{ - 2}}$
  • C
    $1\,\, \times \,{10^{ - 2}}$
  • D
    $7.5\,\, \times \,\,{10^{ - 2}}$

Answer

Correct option: B.
$2.5\,\, \times \,\,{10^{ - 2}}$
b
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, $\mathrm{F}=2 \eta \mathrm{A} \frac{\mathrm{dv}}{\mathrm{dz}}=2 \times \eta \times(0.5) \frac{0.5}{1.25 \times 10^{-2}}$

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

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