Physics - Fluid Question with Solution | TestHub

The terminal velocity of a spherical body in a viscous liquid is given by Stokes' law:

$v_t=\frac{2}{9}\frac{r^2(\rho -\sigma )g}{\eta }$

For the same material and liquid, the terminal velocity is directly proportional to the square of the radius:

$v_t\propto r^2$

$\frac{v_{t2}}{v_{t1}}={\left(\frac{r_2}{r_1}\right)}^2$

Substituting the given values:

$\frac{v_{t2}}{32}={\left(\frac{0.5}{2}\right)}^2$

$\frac{v_{t2}}{32}={\left(\frac{1}{4}\right)}^2=\frac{1}{16}$

$v_{t2}=\frac{32}{16}=2\text{cm/s}$

Answer: $2\text{cm/s}$