Five solid spheres,each of mass $m$ and radius $r$,are arranged as shown in the figure. The axis of rotation $A-A'$ passes through the centers of three spheres. Calculate the moment of inertia of the system about the axis of rotation $A-A'$. (in $m r^2$)

Match the following columns ($R=$ radius,$k=$ radius of gyration):

Column $I$	Column $II$
$(A)$ 'k' for a solid sphere rotating about its tangent	$(P)$ $\sqrt{2}R$
$(B)$ 'k' for a ring rotating about its tangent perpendicular to its plane	$(Q)$ $\frac{R}{2}$
$(C)$ 'k' for a uniform solid right circular cone rotating about its central axis	$(R)$ $\frac{\sqrt{7}}{\sqrt{5}}R$
$(D)$ 'k' for a uniform disc rotating about its diameter	$(S)$ $\frac{\sqrt{3}}{\sqrt{10}}R$

$A$ wire of length $l$ and mass $m$ is bent in the form of a rectangle $ABCD$ with $(AB/BC) = 2$. The moment of inertia of this wire about the side $BC$ is

Two circular discs $A$ and $B$ are of equal masses and thickness but made of metals with densities ${d_A}$ and ${d_B}$ $({d_A} > {d_B})$. If their moments of inertia about an axis passing through their centres and normal to the circular faces are ${I_A}$ and ${I_B}$ respectively,then:

$A$ wire of mass $m$ and length $l$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is:

$A$ light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is