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
$\frac{4}{3} \pi R^{3}=1000 \times \frac{4}{3} \pi r^{3}$
$\Rightarrow R =10 r$
Potential of small drop
$V=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{r} \ldots $ (i)
Potential of bigger drop
$V=\frac{1}{4 \pi \varepsilon_{0}} \frac{1000 q}{R} $
$V=\frac{1}{4 \pi \varepsilon_{0}} \times 1000 \times \frac{q}{10 r} \ldots$ (ii)
From Eqs. (i) and (ii), we get
$V =100 \,V$.