$A$ 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:

Write the conditions for the equilibrium of a rigid body.

$A$ heavy iron bar of mass $12 \,kg$ has one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ}$ with the horizontal. The weight experienced by the man is:

$A$ 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.

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 $g=10\,m/s^2$)

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: $(g = 10 \ m/s^2)$ (in $kg$)