Physics - Fluid Question with Solution | TestHub

Let $T$ be the surface tension of water.

Surface energy of the bigger drop, $E=4\pi R^{2}T$

Surface energy of $n$ smaller drops, $E_i=n(4\pi r^{2}T)$

Energy loss during the formation of the bigger drop is given by:

$\Delta E=E_i-E$

Given that the energy loss is $3E$:

$E_i-E=3E$

$E_i=4E$

Substituting the expressions for $E_i$ and $E$:

$n(4\pi r^{2}T)=4(4\pi R^{2}T)$

$n{r}^2=4R^2$

$n=\frac{4R^2}{r^2}$

Answer: $\frac{4R^2}{r^2}$