Q108 / 125 · BITSAT 2015 · Physics
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 $y=a$.
- Correct answerA$\frac{\eta k}{a}$
- B$\frac{\eta}{k a}$
- C$\frac{\eta a}{k}$
- DNone of these
Solution
Newton's law of viscosity, $F=\eta A \frac{d v}{d y}$
$$
\begin{array}{l}
\text { Stress }=\frac{F}{A}=\eta\left(\frac{d v}{d y}\right)=\eta k\left(\frac{4 y}{a^{2}}-\frac{3 y^{2}}{a^{3}}\right) \\
\text { At } y=a, \text { stress }=\eta k\left(\frac{4}{a}-\frac{3}{a}\right)=\frac{\eta k}{a}
\end{array}
$$
Hence, the correct answer is option: 'A'.