Two discs $A$ and $B$ each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc $A$ 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 $2.7 \, \text{kg m}^2$.

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing through the edge of the disc and normal to the disc is

$A$ uniform circular disc of radius $R$ and mass $M$ is rotating about an axis perpendicular to its plane and passing through its centre. $A$ small circular part of radius $R/2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

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

The moment of inertia of a square loop made of four uniform solid cylinders,each having radius $R$ and length $L$ $(R < L)$,about an axis passing through the midpoints of opposite sides,is (Take the mass of the entire loop as $M$):