As shown in the figure,a person holds a book between their finger and thumb (the book is held at the corner). If the weight of the book is $W$,what is the torque exerted by the person on the book?

$A$ hollow tilted cylindrical vessel of negligible mass rests on a horizontal plane as shown. The diameter of the base is $a$ and the side of the cylinder makes an angle $\theta$ with the horizontal. Water is then slowly poured into the cylinder. The cylinder topples over when the water reaches a certain height $h$,given by

$A$ non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are $36.9^{\circ}$ and $53.1^{\circ}$ respectively. The bar is $2 \; m$ long. Calculate the distance $d$ of the centre of gravity of the bar from its left end.

Write the conditions for the equilibrium of a rigid body.

$A$ uniform metal plate shaped like a triangle $ABC$ has a mass of $540 \,g$. The lengths of the sides $AB, BC$,and $CA$ are $3 \,cm, 5 \,cm$,and $4 \,cm$,respectively. The plate is pivoted freely about the point $A$. What mass must be added to a vertex so that the plate can hang with the long edge $(BC)$ horizontal?

Write the condition for rotational equilibrium and translational equilibrium.