$A$ 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

$A$ 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?

$A$ 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 $kg$)

$A$ metre scale is supported on a wedge at its centre of gravity. $A$ body of weight '$W$' is suspended from the $20 \text{ cm}$ mark and another weight of $25 \text{ g-wt}$ is suspended from the $74 \text{ cm}$ mark to balance it, and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is: (in $\text{ g-wt}$)

$A$ $V$-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?

$A$ 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