Three identical thin rods,each of length $l$ and mass $M$,are joined together to form the letter $H$. What is the moment of inertia of the system about one of the vertical sides of the $H$?

The moment of inertia of a uniform ring of mass $M$ and radius $r$ about a tangent in its own plane is:

Moment of inertia of a body about two perpendicular axes $X$ and $Y$ in the plane of the lamina are $20 \text{ kg m}^2$ and $25 \text{ kg m}^2$ respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of $X$ and $Y$ axes is:

Calculate the moment of inertia of an annular disc about an axis tangent to the outer circle and lying in the plane of the disc. The mass of the disc is $M$,the inner radius is $R_1$,and the outer radius is $R_2$.

$A$ circular plate of mass $M$ and radius $R$ has its density varying as $\rho(r) = \rho_0 r$,where $\rho_0$ is a constant and $r$ is the distance from its center. The moment of inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $I = aMR^2$. The value of the coefficient $a$ is:

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is: