We have two spheres,one solid and one hollow. Their moments of inertia about their respective diameters are equal. The ratio of their radii will be:

The radius of gyration of a solid sphere of radius $R$ and mass $M$ about its diameter is $K_d$ and that about a tangent of a solid sphere is $K_t$. The ratio of $K_d$ to $K_t$ is

The figure shows the variation of the moment of inertia of a uniform rod about an axis passing through its centre and inclined at an angle $\theta$ to the length of the rod. The moment of inertia of the rod about an axis passing through one of its ends and making an angle $\theta = \frac{\pi}{3}$ with the rod will be ........ $kg-m^2$.

$Assertion$ : $A$ 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.

Three bodies have equal masses $m$. Body $A$ is a solid cylinder of radius $R$,body $B$ is a square lamina of side $R$,and body $C$ is a solid sphere of radius $R$. Which body has the smallest moment of inertia about an axis passing through their centre of mass and perpendicular to the plane (in case of lamina)?

Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes in such a way that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is