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# 125 drops of water of same radius and same charge combine to form a big drop. Ration of potential of big drop to the potential of small drop.

$(A)\;25 \\ (B)\;\frac{1}{25} \\ (C)\; 1 \\ (D)\;125$

Potential on small drop (V) $=\large\frac{1}{4 \pi \in _0} \frac{q}{r}$
Volume of 125 small drops = Volume of big drop
=> $125 \times \large\frac{4}{3} \pi r^3= \large\frac{4}{3}$$\pi R^3$
=> $R= 5r$
Potential on big drop,
$V'= \large\frac{1}{4 \pi \in _0} \frac{Q}{R}$
$\quad= \large\frac{1}{4 \pi \in _0} \frac{125 q}{5r}$
$\quad=25 V$
Hence A is the correct answer.

edited Jul 31, 2014