Question

Eight drops each of radius $r$ and charge of are merged to form a single. The ratio of the potentional of big drop to small 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 each of radius $=r$

$V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}$

$V$ $\alpha$ $\frac{1}{r}$

$\frac{4}{3}\pi r^3=$ Volume of the small drop

$\frac{4}{3}\pi R^3=$ Volume of the big drop

$\frac{V_1}{V_2}=2^2\frac{2^3}{2}\frac{8}{2}$

or, $V_1:V_2=4:1$