M.I of a solid sphere about its diameter is$64{\text{\hspace{0.17em}kg\hspace{0.17em}m}}^{\text{2}}$. If that sphere is recast into 8 identical small spheres, then M.I of such small sphere about its diameter is

: given n = 8

 radius of smaller sphere

$\therefore \text{r}=\frac{\text{R}}{{\left(\text{8}\right)}^{\text{1/3}}}=\frac{\text{R}}{{\left({\text{2}}^3\right)}^{\text{1/3}}}$

$\text{r}=\frac{\text{R}}{\text{2}}$

M.I of solid about diametric axis$=\frac{2}{5}{\text{MR}}^{\text{2}}=64{\text{\hspace{0.17em}kgm}}^{\text{2}}$

M.I of small sphere after recasting

$=\frac{2}{5}\left(\frac{\text{M}}{\text{8}}\right){\left(\frac{\text{R}}{\text{2}}\right)}^2=\frac{2}{5}{\text{MR}}^{\text{2}}\times \frac{1}{32}=\frac{64}{32}=2{\text{\hspace{0.17em}kgm}}^{\text{2}}$