Question

$I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center. Where $R$ is the radius of the dise. The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$. The value of $x$ is______

Answer 1

$I _{ cm }=\frac{ mR ^2}{2}$
$ I _{ AB }=\frac{ mR ^2}{2}+ m \left(\frac{2 R }{3}\right)^2=\frac{17}{18} mR ^2 $
$ \frac{ I _{ AB }}{ I _{ cm }}=\frac{17}{9} \Rightarrow x =17$