Question

Two circular discs of same mass and same radius are shaped like a convex and a concave lens respectively . If both are rotated about an axis perpendicular to their planes and passing through their centers , which one will have a greater moment of inertia ? Give reason

Answer 1

Answer:

The concave lens will have greater moment of inertia.

Explanation:

In case of convex lens the mass is concentrated at the center but in case of concave lens the mass is concentrated at the periphery.

So the concave lens is thin at its center and thick at the outer edges,

Hence the concave lens will have greater moment of inertia.

I hope this answer is helpful to you, please feel free to ask any doubts in the comment section.

Answer 2

Answer:

Concave lens.

Explanation:

Moment of inertia is directly proportional to mass and square of mass distance from fixed line.

MI ∝ Mass * (Distance of mass)²

In our case, the axis is the fixed line, which is in the center of the disc, perpendicular to the plane.

Now for a concave lens more mass in outer edge than convex. For a convex lens more mass is near its center.

Hence the square of mass distance factor is more for a concave lens.

Hence moment of inertia is more for a concave lens.