Physics - Rotation Question with Solution | TestHub

Volume of disc is A.d$=\pi .R^2\times \frac{R}{6}=\frac{R^3\times \pi }{6}$

Moment of inertia of disc is$I=\frac{1}{2}M{R}^2$

When the disk is remolded in solid sphere of volume V having radius r, then

$\frac{\pi R^3}{6}=\frac{4}{3}\times \pi r^3\Rightarrow \frac{R^3}{6}\times \frac{3}{4}=r^3$

$\therefore r^3=\frac{R^3}{8}\Rightarrow r=\frac{R}{2}$

Moment of inertia of sphere is given by$\frac{2}{5} M.r^2=\frac{2}{5}\times M.\frac{R^2}{4}=\frac{M{R}^2}{10}=\frac{M{R}^2}{2}\times \frac{1}{5}=\frac{I}{5}$