When it is said that body is in mechanical equilibrium ?

A uniform rod of length $L$ and weight $W$ is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached a distance $L /4$ from the right end. The tension in the second rope is 

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $10\, g$ are put one on the top of the other at the $10.0\, cm$ mark the scale is found to be balanced at $40.0\, cm$ mark. The mass of the metre scale is found to be $x \times 10^{-2}$ $kg$. The value of $x$ is

A uniform rod of length $'l'$ is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed $\omega$ the rod makes an angle $\theta$ with it (see figure). To find $\theta$ equate the rate of change of angular momentum (direction going into the paper ) $\frac{ m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta$ about the centre of mass $(CM)$ to the torque provided by the horizontal and vertical forces $F_{H}$ and $F_{V}$ about the CM. The value of $\theta$ is then such that:

A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$, the initial angular acceleration of the rod will be 

Write the condition for rotational equilibrium and translational equilibrium.