1000 small water drops each of radius r and charge q coalesces together to form one big spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of:

100

The correct answer is Option (2) → 100

Volume of each small drop,

$V_{small}=\frac{4}{3}πr^3$

Total volume of large drop, (R - Radius of large drop)

$V_{large}=N×\frac{4}{3}πr^3=1000×\frac{4}{3}πr^3$

$⇒×\frac{4}{3}πR^3=1000×\frac{4}{3}πr^3$

$⇒R=10r$

The Potential V of a spherical drop,

$V=\frac{kq}{R}=\frac{k×1000q}{10r}$

$∴\frac{V_{large}}{V_{small}}=\frac{\frac{k×1000q}{10r}}{\frac{kq}{r}}=100$