Discussion
If a particle is subjected to a system of coplanar and concurrent forces in X-Y plane, the vector equation must satisfy :
Answer: D
The particle must satisfy both \(\Sigma f_{x} = 0\) and \(\Sigma f_{y} = 0\).
For a particle in equilibrium under coplanar concurrent forces, the vector sum of the forces must be zero, \(\Sigma \vec{F} = 0\). In the X-Y plane that one vector equation splits into two scalar equations, one along each axis.
If only \(\Sigma f_{x} = 0\) held, a resultant along Y would remain, and the particle would accelerate in that direction; the same is true the other way round. The first option, with \(\Sigma f_{y} \neq 0\), describes a particle that is not in equilibrium at all. No moment equation is needed, because concurrent forces all pass through one point.
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