Question

$512$ identical drops of mercury are charged to a potential of $2V$ each. The drops are joined to form a single drop. The potential of this drop is $V.$

Answer 1

Let charge on each drop $=q$
radius $=r$
$v=\frac{k q}{r}$
$2=\frac{kq}{r}$
radius of bigger
$\frac{4}{3}\pi R^{3}=512\times \frac{4}{3}\pi r^{3}$
$R=8r$
$v=\frac{k \left(\right. 512 \left.\right) q}{R}=\frac{512}{8}\frac{k q}{r}=\frac{512}{8}\times 2$
$=128\,V$