Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of…
Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27
small spheres of same diameter. The moment of inertia of each new sphere is
$\frac{\text { I }}{243}$
$\frac{\text { I }}{122}$
$\frac{\mathrm{I}}{31}$
$\frac{\mathrm{I}}{62}$
Solution
When the solid sphere is cast into 27 smaller spheres:
- Mass of each small sphere: $m=\frac{M}{27}$
- Radius of each small sphere: $r=\frac{R}{3}$
- Moment of inertia of each small sphere:
$I_{\text {small }}=\frac{2}{5} m r^2=\frac{I}{243}$
$\frac{I}{243}$