$A$ 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 mass $M = 1 \ kg$ and length $L = 1 \ m$ is suspended horizontally by two ideal strings as shown in the figure. The strings are attached at a distance of $1/3 \ m$ from each end. First, a mass $m_1$ is suspended from the left end while keeping the rod horizontal. Then, a second mass $m_2$ is suspended from the right end, again keeping the rod horizontal. What is the maximum total mass $(m_1 + m_2)$ that can be suspended in this way while maintaining the horizontal orientation of the rod?

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 ............ $kg$.

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

$A$ 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

$A$ 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 $(T_1/T_2)$.