Question

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

• A. v
• B. 2 v
• C. 4 v
• D. 9 v

Answer 1

Answer: (C)

4 v

Answer 2

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