A spherical drop of liquid splits into 1000 identical spherical...

Let $R$ be the radius of bigger drop and $r$ be the radius of smaller drop.

Here, volume will remain conserved, so ${V}_{R} = {V}_{r}$.

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

$⇒ R = 10r$

As surface energy is stated as $u = SA$, here, $S$ is surface tension and $A$ is surface area.

Thus, ${u}_{i} = S$\left(4\pi{R}^{2}\right)$and {u}_{f} = S\left(4\pi{r}^{2}\right) \times 1000$

The ratio is $\dfrac{{u}_{f}}{{u}_{i}} = \dfrac{1000{r}^{2}}{{R}^{2}}$

$⇒ \dfrac{{u}_{f}}{{u}_{i}} = \dfrac{10}{1}$

Hence, the value of $x = 1$.