Which of the following represents the correct mathematical expression for the theorem of perpendicular axes in rotational mechanics (where Z-axis is perpendicular to the X-Y plane)?

The moment of inertia of a rigid body depends on:

Consider a flywheel of mass 10 kg, uniform thickness 15 mm, and radius 100 mm. If it rotates at 300 RPM, then the kinetic energy of the flywheel (in Joules) is:

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If the angular momentum of this system is L about an axis passing through its centre of mass and perpendicular to the rod, then the angular velocity of the system is: