Question

Twenty seven identical mercury drops each charged to $10V$, are allowed to form a big drop. The potential of the big drop is

• A. $90V$
• B. $9V$
• C. $900V$
• D. $270V$

Answer 1

Answer: (A)

Voltage of each mercury drop $=10V$
$\Rightarrow \frac{kq}{r}=10V$
$\Rightarrow q=\frac{10r}{k}$

$totalcharge=\frac{27\times 10r}{k}$
Equating volumes to find radius of bigger charge,

$\frac{4}{3}\pi \left(R^3\right)=27\cdot \frac{4}{3}\pi r^3$

$R=3r$
final voltage$=\frac{kq}{R}=\frac{k\times 27\times 10r}{k\times 3r}$
$=90V$