A large number of liquid drops each of radius r coalesce to form a...

$n \times \dfrac{4}{3}\pi{r}^{3} = \dfrac{4}{3}\pi{R}^{3}$

$∴ n = \dfrac{{R}^{3}}{{r}^{3}} . . . . .$\left(i\right)$</p><p>$KE = {U}_{i} - {U}_{f}$</p><p>$= n \times 4\pi{r}^{2}T - 4\pi{R}^{2}T$</p><p>$= 4\piT ( n{r}^{2} - {R}^{2} )$</p><p>$= 4\piT{R}^{2}\left(\dfrac{R}{r} - 1\right)$from \left(i\right)$

$\dfrac{1}{2}\left(\dfrac{4}{3}\pi{R}^{3} \cdot ρ\right){υ}^{2} = 4\piT{R}^{2}\left(\dfrac{R}{r} - 1\right)$

$\dfrac{Rρ{υ}^{2}}{6} = T\left(\dfrac{R}{r} - 1\right)$

$\dfrac{ρ}{6}{υ}^{2} = T\left(\dfrac{1}{r} - \dfrac{1}{R}\right)$

$υ = \sqrt{\dfrac{6T}{ρ}\left(\dfrac{1}{r} - \dfrac{1}{R}\right)}$