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  4. A sphere of radius R is gently dropped into liquid of viscosity η in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2 R when dropped into the same liquid, will attain its terminal velocity

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Q. A sphere of radius $R$ is gently dropped into liquid of viscosity $ \eta $ in a vertical uniform tube. It attains a terminal velocity $v$. Another sphere of radius $2\,R$ when dropped into the same liquid, will attain its terminal velocity

J & K CETJ & K CET 2008Mechanical Properties of Fluids

Solution:

Terminal velocity $v \propto r^{2}$
$\therefore \frac{v'}{v}=\frac{(2 R)^{2}}{(R)^{2}}$
or $v' = 4\,v$