$A$ metal rod of weight $W$ is supported by two parallel knife-edges $A$ and $B$. The rod is in equilibrium in a horizontal position. The distance between the two knife-edges is $r$. The centre of mass of the rod is at a distance $x$ from $A$. The normal reaction on $A$ is

$A$ metre stick is balanced on a knife edge at its centre. When four coins, each of mass $2 \,g$, are placed one on top of the other at the $10.0 \,cm$ mark, the stick is found to be balanced at the $46.0 \,cm$ mark. The mass of the metre stick is: (in $\,g$)

$A$ uniform metal plate shaped like a triangle $ABC$ has a mass of $540 \,g$. The lengths of the sides $AB, BC$,and $CA$ are $3 \,cm, 5 \,cm$,and $4 \,cm$,respectively. The plate is pivoted freely about the point $A$. What mass must be added to a vertex so that the plate can hang with the long edge $(BC)$ horizontal?

$A$ weightless rod is acted on by upward parallel forces of $2N$ and $4N$ at ends $A$ and $B$ respectively. The total length of the rod $AB = 3m$. To keep the rod in equilibrium,a force of $6N$ should act in the following manner:

$A$ uniform meter scale of mass $m$ is suspended by two vertical strings at its ends as shown in the figure. $A$ mass $m$ is placed at the $80 \ cm$ mark. Find the ratio of the tension forces in the strings $(T_1/T_2)$.

Persons $A$ and $B$ are standing on the opposite sides of a $3.5 \,m$ wide water stream which they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However,each plank is only slightly longer than $3 \,m$. So,they decide to arrange them together as shown in the figure. With $B$ (mass $17 \,kg$) standing on one end of the plank,the maximum mass of $A$,who can walk over the plank is close to ............ $kg$.