# 27 similar drops of mercury are maintained

Question:

27 similar drops of mercury are maintained at $10 \mathrm{~V}$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is _____ times that of a smaller drop.

Solution:

(243)

For self energy of sphere (conducting) $U=\frac{k q^{2}}{2 r}$

For small drop $\rightarrow U_{i}=\frac{k q^{2}}{2 r}$ ......(1)

After combine small drops volume remains same as bigger drop

$\therefore \quad \frac{4}{3} \pi r^{3} \times n=\frac{4}{3} \pi R^{3}$

$\mathrm{R}=(\mathrm{n})^{\frac{1}{3}} \mathrm{r} \quad \ldots \ldots \ldots(2)$           .....(2)

For large drop $\rightarrow U_{f}=\frac{k(n q)^{2}}{2 \times 3 R}$         ......(3)

From equation (1),(2),(3)

$\frac{U_{f}}{U_{i}}=(n)^{5 / 3}$

$\Rightarrow(27)^{5 / 3}$

\\$\Rightarrow 2