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.

A uniform ladder of length $L$ and mass $m_1$ rests against a frictionless wall. The ladder makes an angle $\theta$ with the horizontal.
(a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when a firefighter of mass $m_2$ is at a distance $x$ from the bottom.

(b) If the ladder is just on the verge of slipping when the firefighter is a distance $d$ from the bottom, what is the coefficient of static friction between ladder and ground?