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  4. Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body falling in a liquid and viscosity η of the liquid?

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Q. Which of the following diagrams correctly shows the relation between the terminal velocity $v_{T}$ of a spherical body falling in a liquid and viscosity $\eta$ of the liquid?

WBJEEWBJEE 2020

Solution:

At terminal speed.
$V_{T}=\frac{2 r^{2}}{9 \eta}\left(\rho_{S}-\rho_{L}\right) g$ (Assuming other factor constant)
So, $V_{T} \propto \frac{1}{\eta}$ (rectangular hyperbola)