Parallel and Perpendicular Axis Theorem — MCQ Practice

A uniform rod of mass $M$ and length $L$ is pivoted at one end. Its moment of inertia about an axis perpendicular to the rod and passing through the pivot is:

A uniform circular disc of mass $M$ and radius $R$ has a moment of inertia $I_0$ about an axis passing through its center and perpendicular to its plane. What is its moment of inertia about an axis passing through its diameter?

A thin square plate of mass $M$ and side $a$ has a moment of inertia $I_x = \frac{1}{12}Ma^2$ about an axis passing through its center and parallel to one of its sides. What is its moment of inertia about an axis passing through one of its corners and perpendicular to its plane?

Which of the following statements is TRUE regarding the Perpendicular Axis Theorem?

A uniform ring of mass $M$ and radius $R$ has a moment of inertia $MR^2$ about an axis passing through its center and perpendicular to its plane. What is its moment of inertia about a tangent in its plane?

A solid cylinder of mass $M$, radius $R$, and length $L$ has a moment of inertia $I_{CM} = \frac{1}{2}MR^2$ about its own axis (passing through its center and along its length). What is its moment of inertia about an axis parallel to its own axis and passing through a point on its surface?