Physics - Rotation Question with Solution | TestHub

According to the parallel axis theorem, the moment of inertia of a body about any axis is given by:

$I=I_{cm}+M{d}^2$

where $I_{cm}$ is the moment of inertia about a parallel axis passing through the center of mass, $M$ is the mass of the body, and $d$ is the perpendicular distance between the two axes.

For the given uniform circular disc, the center of mass lies at point A. Thus, $I_{cm}=I_A$.

To maximize the moment of inertia $I$, the distance $d$ from the center of mass must be maximum.

From the given figure, the distances of the points from the center A are such that point B is on the circumference, while points C and D lie inside the disc. Therefore, the distance is maximum for point B ($d=R$).

Hence, the moment of inertia is maximum about an axis perpendicular to the disc and passing through point B.

Answer: B