For equilibrium of the particle what must be the forces acting on it?

A massless string is wrapped round a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be

$ABC$ is an equilateral triangle with $O$ as its centre. $\vec F_1, \vec F_2 $and $\vec F_3$ represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of  $\vec F_3$ is

The moment of inertia of a solid flywheel about its axis is $0.1\,kg-m^2$. A tangential force of $2\,kg\,wt$. is applied round the circumference of the flyweel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m,$ find the angular acceleration of the solid fly wheel (in $rad/sec^2$)

An object of mass $8\,kg$ is hanging from one end of a uniform rod $CD$ of mass $2\,kg$ and length $1\,m$ pivoted at its end $C$ on a vertical wall as shown in figure. It is supported by a cable $A B$ such that the system is in equilibrium. The tension in the cable is $............\,N$ (Take $g=10\,m / s ^2$ )

A thin rod $MN$, free to rotate in the vertical plane about the fixed end $N$, is held horizontal . When the end $M$ is released the speed of this end, when the rod makes an angle $\alpha $ with the horizontal, will be proportional to ( see figure)