Physics - Rotation Question with Solution | TestHub

Given the moment of inertia of the disc about its diameter is $I_d=\frac{M{R}^2}{4}$.

By the perpendicular axis theorem, the moment of inertia of the disc about an axis passing through its center and perpendicular to its plane is $I_c=I_d+I_d=\frac{M{R}^2}{4}+\frac{M{R}^2}{4}=\frac{M{R}^2}{2}$.

By the parallel axis theorem, the moment of inertia of the disc about an axis perpendicular to its plane and passing through a point on its edge is $I=I_c+M{R}^2$.

Substituting the value of $I_c$, we get $I=\frac{M{R}^2}{2}+M{R}^2=\frac{3}{2}M{R}^2$.

Comparing this with the given expression $\frac{x}{2}M{R}^2$, we get $x=3$.

Answer: $3$