Question

Eight small drops, each of radius $r$ and having same charge $q$ are combined to form a big drop. The ratio between the potentials of the bigger drop and the smaller drop is

• A. $8:1$
• B. $4:1$
• C. $2:1$
• D. $1:8$

Answer 1

The correct option is B $4:1$

eight drops radius $r$

so, volume $8\times \frac{4}{3}\Pi r^3$

$=$ volume of bigger drop

$=\frac{4}{3}\Pi r^3$

so, $R=2r$

so, change on smaller is $q$

so, $\frac{\frac{K8q}{R}}{\frac{Rq}{r}}=\frac{8r}{R}$

$=\frac{8r}{2r}$

$=\frac{4}{1}$

option B is correct