The moment of inertia of a thin circular disc about an axis passing through its centre and perpendicular to its plane is $I$. Then, the moment of inertia of the disc about an axis parallel to its diameter and touching the edge of the rim is

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

$A$ solid sphere of radius $R$ has mass $M$. The moment of inertia of the solid sphere about an axis at a distance $\frac{R}{2}$ from the centre is:

$A$ thin wire of length $L$ has a uniform linear mass density $\rho$. It is bent into a circular loop with center $O$. Calculate the moment of inertia of the circular loop about the axis $XX'$ as shown in the figure.

$A$ solid sphere has mass $M$ and radius $R$. Its moment of inertia about a parallel axis passing through a point at a distance $R/3$ from its centre is:

Four identical uniform solid spheres,each of mass $M$ and radius $R$,are placed touching each other in a line as shown in the figure,with centers $A, B, C, D$. Let $I_A, I_B, I_C,$ and $I_D$ be the moment of inertia of the entire system of four spheres about an axis passing through the center of the respective sphere and perpendicular to the plane containing the centers. The difference $|I_A - I_B|$ is: (in $MR^2$)