Question

The capacity of each mercury drop is $10\mu F$ . $64$ such drops are combined to form a single drop. Its resultant capacity is :

• A. $10\mu F$
• B. $20\mu F$
• C. $160\mu F$
• D. $40\mu F$

Answer 1

The correct option is D $40\mu F$

We know capacity of sphere

$C=\frac{Q}{V}$

$C=\frac{Q}{\left(\frac{kQ}{R}\right)}(V=\frac{kQ}{R})$

$C=\frac{R}{k}$

$\therefore$ capacity of each drop $=\frac{R}{k}=10\mu F$

When 64 drops are combined final radius of drop

$R_1=(64{)}^{\frac{1}{3}}R$

$R_1=4R$

$C_1=\frac{R_1}{k}$

$C_1=\frac{4R}{k}$

$C_1=40\mu F$