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

$A$ circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from an iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is:

An annular ring has mass $10 \ kg$ and inner and outer radii are $5 \ m$ and $10 \ m$ respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane 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)

Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

Point masses of $1, 2, 3,$ and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0),$ and $(-2, -2, 0)$ respectively. What is the moment of inertia of this system about the $x$-axis in $kg-m^2$?