Physics - Fluid Question with Solution | TestHub

Terminal velocity is given by $v=\frac{2r^2(\rho -\sigma )}{9\eta }g$ where, $r=$ radius of drop, $\rho =$ density of medium of drop, $\sigma =$ density of surrounding medium $\eta =$ coefficient of viscocity of drop medium. $\Rightarrow \mathrm{v}\propto {\mathrm{r}}^2$, we know area of drop $\propto {\mathrm{r}}^2$ $\Rightarrow \mathrm{v}\propto \mathrm{A}$ (area) $\Rightarrow \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}=\frac{3}{4}$ $\Rightarrow \frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}=\frac{3}{4}$