The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

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?

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	$(b)$ $\frac{2}{5}MR^2$
	$(c)$ $\frac{7}{5}MR^2$

$A$ square plate of mass $M$ and edge $L$ is shown in the figure. The moment of inertia of the plate about the axis in the plane of the plate passing through one of its vertices making an angle $15^{\circ}$ with the horizontal is:

$A$ solid cylinder of length $L = 80 \, \text{cm}$ and mass $M$ has a radius $r = 20 \, \text{cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to the central axis $AB$ (as shown in the figure) is $2.7 \, \text{kg m}^2$.

Consider a thin metal strip of mass $1 \, kg$ and length $5 \, m$. Calculate its moment of inertia about an axis perpendicular to the strip and located at $100 \, cm$ on the strip from one of its ends. (Assume the breadth of the strip is negligible.)