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

$A$ metal bar $70 \; cm$ long and $4.00 \; kg$ in mass is supported on two knife-edges placed $10 \; cm$ from each end. $A$ $6.00 \; kg$ load is suspended at $30 \; cm$ from one end. Find the reactions at the knife-edges. (Assume the bar to be of uniform cross-section and homogeneous.)

$A$ right triangular plate $ABC$ of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through $A$. It is supported by a string at $B$ such that the side $AB$ is horizontal. The reaction at the support $A$ is:

$A$ rigid body in the shape of a $V$ has two equal arms made of uniform rods. What must the angle between the two rods be so that when the body is suspended from one end,the other arm is horizontal?

$A$ metre stick is balanced on a knife edge at its centre. When two coins,each of mass $5\; g$ are put one on top of the other at the $12.0 \;cm$ mark,the stick is found to be balanced at $45.0\; cm$. What is the mass of the metre stick?

$A$ 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.