One circular ring and one circular disc both are having the same mass and radius. The ratio of their moments of inertia about the axis passing through their centre and perpendicular to their planes will be

Determine the ratio of moments of inertia between a circular ring and a circular disc with equal masses and radius using a comparison of their rotation behavior about an axis passing through the center and perpendicular to the planes of the bodies in question.

The moment of inertia of a circular ring depends entirely on its mass being concentrated at its outer edge. For a ring, all the mass is at the same radius, making its moment of inertia proportional to the square of the radius multiplied by its mass.

On the other hand, a circular disc has all of its mass distributed along its entire surface. Some of its masses are closer to the axis of rotation than if all the mass had been concentrated to the outer edge of the disc. Thus its moment of inertia will be lower compared to that of the ring. The result of the moment of inertia in a disc comes from considering its mass distribution:.

Comparing both, the moment of inertia of the ring is twice that of the disc for the same mass and radius. Thus, the ratio of their moments of inertia is 2:1, with the ring having the larger value.

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