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List of top Physics Questions on Moment Of Inertia asked in MHT CET

What is the moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about its diameter?
A solid cylinder and a hollow cylinder, each of mass \( M \) and radius \( R \), are rotating with the same angular velocity \( \omega \). What is the ratio of their rotational kinetic energies \( \left( \frac{K_{\text{hollow}}}{K_{\text{solid}}} \right) \)?
Two spheres are given with radius \( r = 10 \, \text{cm} \), and the distance between them is \( 20 \, \text{cm} \). The axis passes through the midpoint of the distance between the two spheres. What is the moment of inertia of the system?

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \( O \) (the center of mass) and \( O' \) (corner point) is:

A thin circular disc of mass \( M \) and radius \( R \) is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with angular velocity \( \omega \). If another disc of the same dimensions but of mass \( M/2 \) is placed gently on the first disc co-axially, then the new angular velocity of the system is: