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

If torque is calculated relative to a reference point and this point is displaced,does the condition for rotation remain valid?

Shown in the figure is a rigid and uniform one-meter-long rod $AB$ held in a horizontal position by two strings tied to its ends and attached to the ceiling. The rod has a mass $m$ and another weight of mass $2m$ is hung at a distance of $75\, cm$ from $A$. The tension in the string at $A$ is $....mg$.

$A$ false balance has unequal arms. An object weighs $X$ when placed in one pan and $Y$ when placed in the other pan. The true weight $W$ of the object is equal to:

An object of mass $8\,kg$ is hanging from one end of a uniform rod $CD$ of mass $2\,kg$ and length $1\,m$ pivoted at its end $C$ on a vertical wall as shown in the figure. It is supported by a cable $AB$ such that the system is in equilibrium. The tension in the cable is $............\,N$ (Take $g=10\,m/s^2$)

For the system to be in equilibrium,the value of mass $m$ should be .......... $kg$.