Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

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

With reference to the figure of a cube of edge $a$ and mass $m$, state which of the following options are correct ($O$ is the centre of the cube):
$(a)$ The moment of inertia of the cube about the $z$-axis is $I_z = I_x + I_y$
$(b)$ The moment of inertia of the cube about the $A$-axis is $I_A = I_z + \frac{ma^2}{2}$
$(c)$ The moment of inertia of the cube about the $B$-axis is $I_B = I_z + \frac{ma^2}{2}$
$(d)$ $I_x = I_z$

Two hollow spheres each of mass $M$ and radius $\frac{R}{2}$ are connected with a massless rod of length $2R$ as shown in the figure. What will be the moment of inertia of the system about an axis $yy'$ passing through the center of one of the spheres and perpendicular to the rod?

The moment of inertia of a rod about an axis passing through its center of mass and perpendicular to it is $\frac{1}{12}ML^2$. If the rod is bent at the middle such that the two halves make an angle of $90^{\circ}$ in the same plane,what will be the moment of inertia of the system about the same axis?

The moment of inertia of a solid sphere about an axis parallel to its diameter and at a distance $x$ from it is represented by $I$. Which of the following graphs shows the variation of $I$ with $x$?