Question

$1000$ drops of water each of radius $r$ and charged to a potential $V$ coalesce together to form a big drop. The potential of big drop will be

• A. 10 V
• B. 100 V
• C. 1000 V
• D. $\frac{V}{100}$

Answer 1

Answer: (B)

Let $R$ be radius of big drop and $r$ of small drop, then volume of big drop
$=1000\times$ volume of small drop
$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\pi r^3$
$\Rightarrow R=10r$
Potential of small drop
$V=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q}{r}\dots$ (i)
Potential of bigger drop
$V=\frac{1}{4\pi {\epsilon }_0}\frac{1000q}{R}$
$V=\frac{1}{4\pi {\epsilon }_0}\times 1000\times \frac{q}{10r}\dots$ (ii)
From Eqs. (i) and (ii), we get
$V=100V$.