If $I_1, I_2$ and $I_3$ are moments of inertia of a solid sphere,a hollow sphere,and a ring of the same mass $M$ and radius $R$ about their respective geometrical axes,which of the following statements holds true?

The figure shows the variation of the moment of inertia of a uniform rod about an axis passing through its centre and inclined at an angle $\theta$ to the length of the rod. The moment of inertia of the rod about an axis passing through one of its ends and making an angle $\theta = \frac{\pi}{3}$ with the rod will be ........ $kg-m^2$.

The moment of inertia of a uniform rod of length $2l$ and mass $m$ about an axis $xx'$ passing through its centre and inclined at an angle $\alpha$ is

What is the radius of gyration? Write its unit and dimensional formula.

$A$ body of mass $m$ and radius of gyration $K$ has an angular momentum $L$. Then its angular velocity is

Two discs have the same thickness. Their radii are $R_1$ and $R_2$ and their densities are $d_1$ and $d_2$. The moment of inertia of the second disc is greater than the first if: