A uniform rod $AB$ is suspended from a point $X$, at a variable distance from $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m, x)$ values is recorded. The appropriate variable that give a straight line, when plotted, are

$ABC$ is an equilateral triangle with $O$ as its centre. $\vec F_1, \vec F_2 $and $\vec F_3$ represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of  $\vec F_3$ is

A mass $'m'$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

Shown in the figure is rigid and uniform one meter long rod $AB$ held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass $'m'$ and has another weight of mass $2m$ hung at a distance of $75\, cm$ from $A$. The tension in the string at $A$ is$....mg$

A uniform meter scale balances at the $40\,cm$ mark when weights of $10\,g$ and $20\,g$ are suspended from the $10\,cm$ and $20\,cm$ marks. The weight of the metre scale is ...... $g$

Can a body will remain in partial equilibrium ? Explain with illustration.