Question

Eight small droplets of mercury of equal radii are charged to the same potential $10V$. If they coalesce to form one big drop, the potential on big drop is:

• A. $10V$
• B. $20V$
• C. $30V$
• D. $40V$

Answer 1

Answer: (D)

$40V$

given potential of each drop $=10V$
$\Rightarrow \frac{kq}{r}=10V$
when $8$ drops are coalesced its volume remains same
$\Rightarrow 8\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3$
$\Rightarrow R=2r$
Now radius of big drop $=2r$ and charge on big drop $=8q$

$\therefore$ Potential of big drop $=\frac{k\left(8q\right)}{2r}$
$=4\times \frac{kq}{r}$

$=40V$