$A$ 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 meter scale is ...... $g$.

If a street light of mass $M$ is suspended from the end of a uniform rod of length $L$ in different possible patterns as shown in the figure,then

$A$ $V$-shaped rigid body has two identical uniform arms. What must be the angle between the two arms,so that when the body is hung from one end,the other arm is horizontal?

$A$ weightless rod is acted on by upward parallel forces of $2N$ and $4N$ at ends $A$ and $B$ respectively. The total length of the rod $AB = 3m$. To keep the rod in equilibrium,a force of $6N$ should act in the following manner:

Persons $A$ and $B$ are standing on the opposite sides of a $3.5 \,m$ wide water stream which they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However,each plank is only slightly longer than $3 \,m$. So,they decide to arrange them together as shown in the figure. With $B$ (mass $17 \,kg$) standing on one end of the plank,the maximum mass of $A$,who can walk over the plank is close to ............ $kg$.

$A$ small ball of mass $m$ is suspended from the ceiling by a string of length $L$. The ball moves along a horizontal circle with constant angular velocity $\omega$, as shown in the figure. The torque about the centre $(O)$ of the horizontal circle is