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

$A$ 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?

$A$ 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:

Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body,which is then pivoted as shown in the figure. If in equilibrium the body is in the shown configuration,the ratio $M/m$ will be

Write the conditions for the equilibrium of a rigid body.

$A$ uniform rod of mass $250 \ g$ having length $100 \ cm$ is balanced on a sharp edge at $40 \ cm$ mark. $A$ mass of $400 \ g$ is suspended at $10 \ cm$ mark. To maintain the balance of the rod,the mass to be suspended at $90 \ cm$ mark is: (in $g$)