Question

$1000$ drops, each other of V volt, are combined to form a big drop, then the ratio of potential of the bigger drop to that of smaller drop is :

• A. $1$
• B. $0$
• C. $100$
• D. $1000$

Answer 1

The correct option is C $100$

We know potential of drop $V=\frac{kq}{R}$
now charge of bigger drop $Q_1=1000Q$

Radius of bigger drop $R_1=(1000{)}^{{}^1{/}_3}R$ (by conservation of volume)
$\Rightarrow R_1=10R.$
potential of bigger drop $V_1=\frac{k{Q}_1}{R_1}$
$V_1=\frac{k\left(1000Q\right)}{10R}$

$V_1=100\frac{kQ}{R}$

$V_1=100\times V$