Consider the situation shown in the figure. $A$ uniform rod of length $L$ can rotate freely about the hinge $A$ in a vertical plane. Pulleys and string are light and frictionless. If the rod remains horizontal at rest when the system is released,then the mass of the rod is:

$A$ uniform rod of length $L$ and weight $W$ is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached at a distance $L/4$ from the right end. The tension in the second rope is

$A$ uniform rod of length $1\, m$ and mass $4\, kg$ is supported on two knife-edges placed $10\, cm$ from each end. $A$ $60\, N$ weight is suspended at $30\, cm$ from one end. The reactions at the knife edges are:

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: $(g = 10 \ m/s^2)$ (in $kg$)

$A$ false balance has unequal arms. An object weighs $X$ when placed in one pan and $Y$ when placed in the other pan. The true weight $W$ of the object is equal to:

$A$ wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However,the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?