Physics - Rotation Question with Solution | TestHub

Moment of inertia of big drop is $I=\frac{2}{5}M{R}^2$ When small droplets are formed from big drop volume of liquid remain same $$\begin{array}{rl}n\frac{4}{3}\pi r^3& =\frac{4}{3}\pi R^3\\ n^{1/3}r& =R\text{ as }n=8\Rightarrow r=\frac{R}{2}\end{array}$$ Mass of each small droplet $=\frac{M}{8}$ $\therefore$ Moment of inertia of each small droplet $$\begin{array}{l}=\frac{2}{5}\left[\frac{M}{8}\right]{\left[\frac{R}{2}\right]}^2\\ =\frac{1}{32}\left[\frac{2}{5}M{R}^2\right]=\frac{I}{32}\end{array}$$