Explanation

(a) Let $R\ and\ r$ be the radii of bigger and each smaller drop respectively
$\therefore\ \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\pi R^{3} = 8 \times \frac{4}{3}\pi r^{3}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R = 2r$ …(i)
The capacitance of a smaller spherical drop is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C = 4\pi\varepsilon_{0}r$ …(ii)
The capacitance of bigger drop is
$C^{'} = 4\pi\varepsilon_{0}R$
= $2 \times 4\pi\varepsilon_{0}r$ ($\because R = 2r$)
$= 2C\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack From\ Eq.(ii)\rbrack$
$C = \frac{C^{'}}{2}$
$= \frac{1}{2}\mu F\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because C^{'} = 1\mu F)$