Find the moment of inertia of a spherical ball of mass $m$ and radius $r$ attached at the end of a straight rod of mass $M$ and length $l$, if this system is Ifee to rotate about an axis passing through the end of the rod (end of the rod opposite to sphere).

Find moment of inertia of a triangular lamina of mass $M$ about the axis of rotation $AB$ shown in figure.

A uniform circular disc of radius $R$ has a sector of angle ${90}^{\mathrm{o}}$ removed from it. Mass of the remaining disc is $M$. Write the moment of inertia of the remaining disc about the axis $xx$ shown in figure.

A uniform rectangular plate has side length $l$ and $2l$. The plate lies in $x$- $y$ plane with its centre at origin and sides parallel to $x$- and $y$-axes. The moment of inertia of the plate about an axis passing through a vertex (say $A$) perpendicular to the plane of the figure is $I_0$. Now the axis is shifted parallel to itself so that moment of inertia about it remains $I_0$. Write the locus of point of intersection of the axis with $x$- $y$ plane.

A beam of weight $W$ supports a block of weight $W.$ The length of the beam is $L$ and weight is at a distance $L/4$ from the left end of the beam. The beam rests on two rigid supports at its ends. Find the reactions of the supports.

A uniform rod of length $l$ and mass $m$ is hung from two strings of equal length from a ceiling as shown in figure. Determine the tensions in the strings.