Physics - Fluid Question with Solution | TestHub

We know that terminal velocity is

given by

${\text{V}}_{\text{T}}=\frac{2}{9\text{n}}{\text{r}}^2\left({\text{ρ}}_{\text{s}}-{\text{ρ}}_{\text{l}}\right)$

$\therefore {\text{V}}_{\text{T}}\propto \mathrm{r}{}^2$

$\therefore \frac{9}{4}={\left(\frac{\mathrm{r}{}_1}{\mathrm{r}{}_2}\right)}^2$

$\therefore \frac{r_1}{r_2}=\frac{3}{2}$

$\therefore \frac{{\text{V}}_1}{{\mathrm{V}}_2}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{3}{2}\right)}^3$

$\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=27\text{:}8$