Moment of Inertia — MCQ Practice

A uniform thin rod of mass $M$ and length $L$ is pivoted at one end. What is its Moment of Inertia about an axis perpendicular to the rod and passing through this pivot point?

A thin circular ring of mass $M$ and radius $R$ is rotating about an axis passing through its center and perpendicular to its plane. Its Moment of Inertia is $MR^2$. What is its Moment of Inertia about an axis tangent to the ring and lying in its plane?

A solid sphere of mass $M$ and radius $R$ rolls without slipping on a horizontal surface. What is its Moment of Inertia about the axis of rotation (the instantaneous axis of rotation at the point of contact)?

Two particles, each of mass $m$, are connected by a massless rod of length $L$. What is the Moment of Inertia of this system about an axis perpendicular to the rod and passing through its center?

A thin uniform square plate of mass $M$ and side $a$ lies in the XY-plane. If its Moment of Inertia about the x-axis is $I_x = \frac{1}{12}Ma^2$, what is its Moment of Inertia about an axis perpendicular to the plate and passing through its center?

Which of the following objects, all having the same mass $M$ and radius $R$, will have the largest Moment of Inertia about an axis passing through its center and perpendicular to its plane (or diameter for sphere)?