$A$ 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 $kg$)

$A$ horizontal force $F$ is applied to a block as shown in the figure such that the block remains in a state of rest. Which of the following statements is true?

$A$ 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:

$A$ meter stick is balanced on a knife edge at its centre. When a $10 \ g$ coin is placed on top of the stick at the $12 \ cm$ mark,the stick is found to be balanced at the $45 \ cm$ mark. Then the mass of the meter stick is $.... \ g$.

$A$ uniform metal plate shaped like a triangle $ABC$ has a mass of $540 \,g$. The lengths of the sides $AB, BC$,and $CA$ are $3 \,cm, 5 \,cm$,and $4 \,cm$,respectively. The plate is pivoted freely about the point $A$. What mass must be added to a vertex so that the plate can hang with the long edge $(BC)$ horizontal?

Explain the construction and working of an ideal lever and also explain the principle of moments of force.