$A$ weight $Mg$ is suspended from the middle of a rope whose ends are at the same level. The rope is no longer horizontal. The minimum tension required to completely straighten the rope is ......

$A$ block of $\sqrt{3} \, kg$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension $T$ is $........... \, N$ : (Given $g = 10 \, ms^{-2}$)

Describe the different types of common forces.

Two equal heavy spheres,each of radius $r$,are in equilibrium within a smooth cup of radius $3r$. The ratio of the reaction between the cup and one sphere to that between the two spheres is:

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$,at a height $L$ above the hinge at point $O$. $A$ block of weight $\alpha W$ is attached at the point $P$ of the beam,as shown in the figure. The rope can sustain a maximum tension of $(2 \sqrt{2}) W$. Which of the following statement$(s)$ is(are) correct?

Find the magnitude of the unknown forces $x$ and $y$ if the sum of all forces is zero.