Question

Moment of inertia of big drop is $ I $ . If $ 8 $ droplets are formed from big drop, then moment of inertia of small droplet is

• A. $ \frac{I}{32} $
• B. $ \frac{I}{16} $
• C. $ \frac{I}{8} $
• D. $ \frac{I}{4} $

Answer 1

The Correct Option is A

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 $n \frac{4}{3} \pi r^{3}=\frac{4}{3} \pi R^{3}$ $\Rightarrow n^{1 / 3} r=R$ as $n=8 \Rightarrow r=\frac{R}{2}$ Mass of each small droplet $=\frac{M}{8}$ $\therefore$ Moment of inertia of each small droplet $=\frac{2}{5}\left[\frac{M}{8}\right]\left[\frac{R}{2}\right]^{2}$ $=\frac{1}{32}\left[\frac{2}{5} M R^{2}\right]=\frac{I}{32}$