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

Answer: 128

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