$A$ 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 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 $(T_1/T_2)$.

$A$ 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?

$A$ uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height $a$ $(a < R)$ by applying a force $F$ at its centre $'O'$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $F$ required is

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

Two men are carrying a uniform bar of length $L$ on their shoulders. The bar is held horizontally such that the younger man gets $(1/4)^{th}$ of the load. Suppose the younger man is at the end of the bar,what is the distance of the other man from that end?