Physics - Fluid Question with Solution | TestHub

Let the radius of the initial liquid drop be $R$ and the surface tension be $T$.

The initial surface energy is given by $V=4\pi R^{2}T$.

When the drop is sprayed into $n=1000$ equal droplets of radius $r$, the total volume remains constant.

$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\pi r^3$

$R^3=1000r^3\Rightarrow r=\frac{R}{10}$

The total surface energy of the $1000$ droplets is $E=1000\times 4\pi r^{2}T$.

Substituting $r=\frac{R}{10}$:

$E=1000\times 4\pi {\left(\frac{R}{10}\right)}^{2}T$

$E=1000\times \frac{4\pi R^{2}T}{100}$

$E=10\times (4\pi R^{2}T)=10V$

Answer: 10 V