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:

$A$ 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 . . . . . . .

The moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is .......

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

$A$ solid sphere and a thin-walled hollow sphere have the same mass and the same material. Which of them has a greater moment of inertia about its diameter? ($I_{h} =$ moment of inertia of a hollow sphere about an axis coinciding with its diameter,$I_{s} =$ moment of inertia of a solid sphere about an axis coinciding with its diameter)

$A$ rod has a length of $1 \ m$ and a mass of $0.12 \ kg$. The moment of inertia about an axis passing through its center and perpendicular to its length is ...... $kg \cdot m^2$.