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Two spheres of equal masses but radii $r_1$ and $r_2$ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities is
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We have $\mathrm{v}_{\mathrm{T}}=\frac{2 r^2(\sigma-\rho) g}{9 \eta}$
$\frac{\mathrm{v}_1}{\mathrm{v}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2 \frac{\left(\sigma_1-\rho\right)}{\left(\sigma_2-\rho\right)} ;$ given $\mathrm{m}_1=\mathrm{m}_2 \Rightarrow\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{\sigma_2}{\sigma_1}$
$\frac{\mathrm{v}_1}{\mathrm{v}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2 \frac{\left(\sigma_1-\rho\right)}{\left(\sigma_2-\rho\right)} ;$ given $\mathrm{m}_1=\mathrm{m}_2 \Rightarrow\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{\sigma_2}{\sigma_1}$
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