The moment of inertia of a solid sphere of mass $M$ and radius $R$ about its tangent is:

Three spheres,each of mass $m$ and radius $r$,are placed as shown in the figure. Consider an axis $YY^1$,which is tangent to two spheres (labeled $2$ and $3$) and passes through the diameter of the third sphere (labeled $1$). The moment of inertia of the system consisting of these three spheres about the $YY^1$ axis is:

The moment of inertia of a ring about an axis perpendicular to its plane and passing through its center is $4 \,kg \,m^2$. Its moment of inertia about the tangent in the plane is

Four holes of radius $R$ are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about the $z-$ axis is

$A$ circular disc of mass $9M$ and radius $R$ has a smaller disc of radius $R/3$ cut from it. Calculate the moment of inertia of the remaining portion about an axis passing through the center of the original disc and perpendicular to its plane. (in $MR^2$)

$A$ rigid body of mass $m$ is rotating with angular velocity $\omega$ about an axis at a distance '$a$' from the center of mass $G$. The radius of gyration about an axis passing through $G$ is $K$. The rotational kinetic energy of this body about the new parallel axis will be: