Question

1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. The electric energy gets increased by

• A. 100 times
• B. 200 times
• C. 300 times
• D. 400 times

Answer 1

Answer: (A)

Let $q$ be charge on each small drop of radius $r$. If $R$ is radius of big drop, then
$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\pi r^3$
$\therefore R=10r$
and $C^{\prime }=10C$
Initial energy, $E_1=1000\times \frac{q^2}{2C}$
Final energy, $E_2=\frac{(1000q{)}^2}{2C^{\prime }}$
$\frac{E_2}{E_1}=\frac{1000\times C}{C^{\prime }}=1000\times \frac{1}{10}=100$