= Solution
Let the particle and carrier-fluid <mass densities> be $\rho_p$ and $\rho_f$, with identical density contrast for both species. At small <particle Reynolds number>, balance <Stokes drag law> against submerged weight:
$$
6\pi\mu rW_s=\frac43\pi r^3(\rho_p-\rho_f)g,
\qquad W_s=\frac{2(\rho_p-\rho_f)gr^2}{9\mu}.
$$
Consequently
$$
\boxed{\frac{W_s(r_1)}{W_s(r_2)}=\left(\frac{r_1}{r_2}\right)^2\quad(\operatorname{Re}_p\ll1).}
$$
At large <particle Reynolds number>, use approximately constant <drag coefficient> $C_D$ and <quadratic drag>. Balancing $\frac12C_D\rho_f\pi r^2W_s^2$ against the same submerged weight gives $W_s^2=8(\rho_p-\rho_f)gr/(3C_D\rho_f)$, so
$$
\boxed{\frac{W_s(r_1)}{W_s(r_2)}\simeq\left(\frac{r_1}{r_2}\right)^{1/2}\quad(\operatorname{Re}_p\gg1).}
$$
Both particles must lie in the constant-$C_D$ regime for this simple square-root ratio. More generally it contains an additional factor $\sqrt{C_D(r_2)/C_D(r_1)}$. The speeds are positive downward magnitudes; the signs of the shock velocities below depend on the chosen spatial coordinate.
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