Two lenses of same mass and radius are given one is convex and the other is concave .Which one will have greater momentum of inertia while rotating about an Axis perpendicular to the plane and passing through the optical Centre? Why it is so?

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Solution

Moment of Inertia is directly proportion to the distance between the mass and the axis.
In a convex lens, the centre is thicker. ie, more mass is concentrated at the centre. So the distance between most of the masses and the axis is less.
In a concave lens, the centre is thinner. ie, more mass is concentrated away from the centre. So the distance between most of the masses and the axis is more.

So, a concave lens will have higher moment of inertia when the axis is perpendicular to the plane and passing through the optic centre.

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