Four particles each of mass $m$ are placed at the corners of a square of side length $l.$ The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

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 $kg-m^2$?

$A$ thin metal wire of length $L$ and mass $M$ is bent to form a semicircular ring as shown. The moment of inertia about the axis $XX^1$ passing through its ends is:

Two half rings are joined as shown in the figure. Each half ring has a radius $R$ and mass $M$. The moment of inertia of the system about the axis $XX'$ is

$Assertion$ : $A$ judo fighter,in order to throw his opponent onto the mat,tries to initially bend his opponent and then rotate him around his hip.
$Reason$ : As the mass of the opponent is brought closer to the fighter's hip,the moment of inertia of the opponent about the axis of rotation decreases,which makes it easier to rotate the opponent.

Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?