$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. Their moments of inertia about their diameters are $I_A$ and $I_B$ respectively. Which of the following relations is correct?

Let $M$ and $L$ be the mass and length of a thin uniform rod,respectively. In the $1^{\text{st}}$ case,the axis of rotation passes through the center and is perpendicular to its length. In the $2^{\text{nd}}$ case,the axis of rotation passes through one end and is perpendicular to its length. The ratio of the radius of gyration in the first case to the second case is:

Moment of inertia of a thin uniform rod of length $L$ and mass $M$ rotating about the perpendicular axis passing through its centre is $I$. If the same rod is bent in the form of a ring,its moment of inertia about the diameter is $I_1$. If $I_1 = xI$,then the value of $x$ is:

Two rings of same mass $m$ and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is ............

The moment of inertia of a body is $160 \ kg \ m^2$ and its mass is $10 \ kg$. What will be the radius of gyration in $m$?

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?