Consider a thin walled hoop of uniform material. two axis go through the center of the hoop. one axis is perpendicular to the plane of the hoop and the other axis is parallel to the plane of the hoop. which axis would make the large moment of inertia for the hoop

Explanation:

Moment of Inertia about an axis passing through its center and Perpendicular to its Plane is given by

As all the mass is at radius therefore its moment of inertia is more than the moment of inertia about a axis parallel to the Plane

According to perpendicular axis theorem

and is same due to symmetry

thus

thus Perpendicular z axis will have more moment of inertia

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