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9.1 , fluid mechanics — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics9.1 , fluid mechanics1 Mark
MCQ
Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$. If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$. 
  • ✓
    $\frac{\eta k}{a}$
  • B
    $\frac{\eta}{k a}$
  • C
    $\frac{\eta a}{k}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{\eta k}{a}$
a
(a)

Newton's law of viscosity, $F=\eta A \frac{d v}{d y}$

$\text { Stress }=\frac{F}{A}=\eta\left(\frac{d v}{d y}\right)=\eta k\left(\frac{4 y}{a^2}-\frac{3 y^2}{a^3}\right)$

$\text { At } y=a, \text { stress }=\eta k\left(\frac{4}{a}-\frac{3}{a}\right)=\frac{\eta k}{a}$

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