Question

Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius.

A. A ring about its axis, perpendicular to the plane of the ring.
B. A disc about its axis, perpendicular to the plane of the ring.
C. A solid sphere about one of its diameters
D. A spherical shell about one of its diameters.

Answer 1

The object with the highest moment of inertia when each of them has the same mass and radius is D. a spherical shell about one of its diameters.

Step-by-step explanation:

The moment of inertia depends on the distribution of mass and the axis of rotation. When each of the objects has the same mass and radius, the object with the highest moment of inertia is a spherical shell about one of its diameters.

This can be understood by comparing the moments of inertia for each object using the parallel-axis theorem. The moment of inertia for a spherical shell is given by I = (2/3)MR², which is greater than the moment of inertia for a solid sphere, a disc, and a ring about their respective axes. Therefore, option D, a spherical shell about one of its diameters, has the highest moment of inertia among the given options.