$A$ 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 $kg$)

In a physical balance working on the principle of moments,when $5\, mg$ weight is placed on the left pan,the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

State the principle of moments for a lever.

$A$ uniform rod of length $200 \, cm$ and mass $500 \, g$ is balanced on a wedge placed at $40 \, cm$ mark. $A$ mass of $2 \, kg$ is suspended from the rod at $20 \, cm$ and another unknown mass $'m'$ is suspended from the rod at $160 \, cm$ mark as shown in the figure. Find the value of $'m'$ such that the rod is in equilibrium. $(g = 10 \, m/s^2)$

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

$A$ 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