$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

The moment of inertia of a ring about an axis perpendicular to its plane and passing through its center is $4 \,kg \,m^2$. Its moment of inertia about the tangent in the plane is

Identical rings are arranged in a hexagonal plane pattern such that each ring touches its neighbouring rings. Each ring has mass $M$ and radius $R$. The moment of inertia of the system of seven rings about an axis passing through the centre of the central ring and normal to the plane of all rings is: (in $MR^2$)

The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through its center and normal to its length is $\alpha$. Now,the rod is cut into two equal parts,and these parts are joined symmetrically to form a cross shape. The moment of inertia of the cross about an axis passing through its center and normal to the plane containing the cross is:

The string of a simple pendulum is replaced by a uniform rod of length $L$ and mass $M$. If the mass of the bob of the pendulum is $m$,then for small oscillations its time period would be (assume radius of bob $r << L$):

In the triangular sheet shown,$PQ = QR = l$. If $M$ is the mass of the sheet,what is the moment of inertia about the axis $PR$?