$ ABC$  is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$  are the moment of inertia of the plate about $AB, BC$  and $CA$  respectively. Which one of the following relations is correct

We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$

A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity $\omega _0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is

The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,metre$ rotating about one of its diameter is

Ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively then ratio of moment of inertia will be