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 $\frac{I}{32}$

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 remains 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.
$=\frac{2}{5}\left[\frac{M}{8}\right]{\left[\frac{R}{2}\right]}^2$
$=\frac{1}{32}\left[\frac{2}{5}M{R}^2\right]=\frac{I}{32}$