$A$ horizontal beam is pivoted at $O$ as shown in the figure. Find the mass $m$ to make the scale straight in $kg$.

$A$ wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However,the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

Two persons of equal height are carrying a long uniform wooden beam of length $\ell$. They are at a distance of $\frac{\ell}{5}$ and $\frac{\ell}{3}$ from the nearest ends of the rod. The ratio of the normal reaction at their heads is

An $L$-shaped object,made of two thin rods of uniform mass density and equal length $a$,is suspended from a string as shown in the figure. If $AB = BC = a$,and the angle made by $AB$ with the downward vertical is $\theta$,then:

$A$ $V$-shaped rigid body has two identical uniform arms. What must be the angle between the two arms,so that when the body is hung from one end,the other arm is horizontal?

Write the condition for rotational equilibrium and translational equilibrium.