Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$-direction,the magnitude of the minimum additional force needed is:

$A$ $50 \, kg$ homogeneous smooth sphere rests on a $30^{\circ}$ incline $A$ and bears against a smooth vertical wall $B$. Calculate the contact force at $A$. (Take $g = 10 \, m/s^2$)

When three forces of $50 \, N$,$30 \, N$,and $15 \, N$ act on a body,then the body is

$A$ block of mass $90 \,kg$ is suspended by three strings $A, B$ and $C$ as shown in the figure. Find the tensions in the strings $A, B$ and $C$ respectively. $\left(g=10 \,ms^{-2}, \sin 37^{\circ}=0.6, \cos 37^{\circ}=0.8\right)$

Three forces $\vec{P}, \vec{Q},$ and $\vec{R}$ act at a point in a plane. The angles between $\vec{P}$ and $\vec{Q}$,and $\vec{Q}$ and $\vec{R}$ are $150^{\circ}$ and $120^{\circ}$ respectively. What is the ratio of the magnitudes of the forces $\vec{P}, \vec{Q},$ and $\vec{R}$ if the system is in equilibrium?

Explain the main types of forces with suitable examples.