Find the moment of inertia of the ring shown in the figure about the axis $AB$.

Seven identical coins are rigidly arranged on a flat table in the pattern shown below,so that each coin touches its neighbours. Each coin is a thin disc of mass $m$ and radius $r$. Note that the moment of inertia of an individual coin about an axis passing through its centre and perpendicular to the plane of the coin is $\frac{m r^2}{2}$. The moment of inertia of the system of seven coins about an axis that passes through the point $P$ (the centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is ..........$m r^2$.

The moment of inertia of a thin rod about an axis passing through its center and perpendicular to its length $L$ is $I$. What will be the moment of inertia of a square frame formed by four such rods about an axis passing through its center and perpendicular to the plane of the square (in $I$)?

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Moment of inertia of a solid sphere about its diameter	$(a)$ $\frac{2}{3}MR^2$
$(2)$ Moment of inertia of a solid sphere about a tangent	$(b)$ $\frac{2}{5}MR^2$
	$(c)$ $\frac{7}{5}MR^2$

The moment of inertia of a solid cylinder of mass $M$,length $L = 2R$ and radius $R$ about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is $I_1$,and about an axis passing through one end of the cylinder and perpendicular to the axis of the cylinder is $I_2$. Then:

Two rings of the same radius and mass are placed such that their centers coincide and their planes are mutually perpendicular. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is ...... (where mass $= m$,radius $= r$)