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

Consider the situation shown in the figure. $A$ uniform rod of length $L$ can rotate freely about the hinge $A$ in a vertical plane. Pulleys and string are light and frictionless. If the rod remains horizontal at rest when the system is released,then the mass of the rod is:

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

$A$ $3\; m$ long ladder weighing $20\; kg$ leans on a frictionless wall. Its feet rest on the floor $1\; m$ from the wall as shown in the figure. Find the reaction forces of the wall and the floor.

$A$ meter stick is balanced on a knife edge at its centre. When a $10 \ g$ coin is placed on top of the stick at the $12 \ cm$ mark,the stick is found to be balanced at the $45 \ cm$ mark. Then the mass of the meter stick is $.... \ g$.

$A$ rod of weight $W$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at distance $x$ from $A.$ The normal reaction on $A$ is