One solid sphere $A$ and another hollow sphere $B$ have the same mass and the same outer radii. Their moments of inertia about their diameters are $I_{A}$ and $I_{B}$ respectively. Which of the following relations is correct?

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

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

$A$ circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2}=2$, then $\frac{T_1}{T_2}=\frac{1}{\alpha}$. The value of $\alpha$ is . . . . . . .

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio $1 : 3$. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio:

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is: