Explanation

(a) Moment of inertia of big drop is $I = \frac{2}{5}\ MR^{2}$. When small droplets are formed from big drop volume of liquid remain same
$n\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi R^{3}$
$\Rightarrow$ $n^{\frac{1}{3}}r = R$
as $n = 8$
$\Rightarrow$ $r = \frac{R}{2}$
Mass of each small droplet $= \frac{M}{8}$
$\therefore$ Moment of inertia of each small droplet
$= \frac{2}{5}\left\lbrack \frac{M}{8} \right\rbrack\left\lbrack \frac{R}{2} \right\rbrack^{2}$
$= \frac{1}{32}\left\lbrack \frac{2}{5}MR^{2} \right\rbrack = \frac{I}{32}$