Question

Calculate the energy spent in spraying a drop of mercury of radius $R$ into $N$ droplets all of same size. If the surface tension of mercury is $T$.

Answer 1

Let the radius of the small droplets be $r$ and $\rho$ be the density of mercury.

Mass of the drop must be equal to the total mass of the droplets.

$\therefore$ $\rho \times \frac{4\pi }{3}{R}^3=N\times \frac{4\pi }{3}{r}^3\times \rho$ $⟹R^3=N{r}^3$

Change in surface area $\Delta A=N\times 4\pi r^2-4\pi R^2=4\pi (N{r}^2-R^2)$

$\therefore$ Energy spent $E=T\Delta A=4\pi T(N{r}^2-R^2)$