$A$ 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?

$A$ solid sphere of radius $r = 5 \text{ cm}$ is rotating about an axis at a distance $d = 10 \text{ cm}$ from its center, as shown in the figure. If the radius of gyration about that axis is $\sqrt{x} \text{ cm}$, then the value of $x$ is:

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

The moment of inertia of a solid disc rotating about its diameter is $2.5$ times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and is rotating in a similar way,is $n$ times higher than the moment of inertia of the given ring. Here,$n=$ . . . . . . . Consider all the bodies have equal masses.

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?

The radius of gyration of a rod of length $L$ and mass $M$ about an axis perpendicular to its length and passing through a point at a distance $L/3$ from one of its ends,is :-