Physics - Rotation Question with Solution | TestHub

The moment of inertia of a disc about an axis passing through its center and perpendicular to its plane is given by:

$I_c=\frac{1}{2}M{R}^2$

Using the parallel axis theorem, the moment of inertia about an axis passing through a point at a distance $x$ from the center and perpendicular to the plane is:

$I=I_c+M{x}^2$

Given that $I=M{R}^2$, we can write:

$\frac{1}{2}M{R}^2+M{x}^2=M{R}^2$

$M{x}^2=M{R}^2-\frac{1}{2}M{R}^2$

$M{x}^2=\frac{1}{2}M{R}^2$

$x^2=\frac{R^2}{2}$

$x=\frac{R}{\sqrt{2}}$

Answer: $\frac{R}{\sqrt{2}}$