Equilibrium of concurrent forces at a point A set of forces acting at a single point will be in equilibrium if which condition is satisfied?

Introduction / Context:
Forces that meet at a point are common in pin-jointed structures, cable junctions, and particle mechanics. Recognizing the correct equilibrium condition simplifies problem solving and prevents unnecessary calculations.

Given Data / Assumptions:

• All forces are concurrent at a single point.
• We assume coplanar conditions unless otherwise stated.
• Static equilibrium requires no net acceleration.

Concept / Approach:
For a particle (point) in equilibrium, the vector sum of all external forces must be zero. In 2D, this is equivalent to requiring both ΣF_x = 0 and ΣF_y = 0 simultaneously. Merely having ΣF_y = 0 is insufficient unless ΣF_x = 0 also holds. Angles being “equally inclined” does not guarantee net zero force.

Step-by-Step Solution:
Write vector condition: ΣF = 0.In components: ΣF_x = 0 and ΣF_y = 0.Therefore the correct single statement among options is: “sum of all the forces is zero”.Hence select option (b).

Verification / Alternative check:
If ΣF = 0, the point does not accelerate (Newton’s second law: ΣF = m * a); with m > 0, this implies a = 0, confirming equilibrium.

Why Other Options Are Wrong:

• Equally inclined forces may still produce a nonzero resultant.
• ΣV = 0 alone ignores horizontal components; equilibrium demands both directions be zero.
• “None of these” is incorrect because (b) is correct.

Common Pitfalls:

• Checking only one direction (often vertical) and forgetting horizontal balance.

Final Answer:
sum of all the forces is zero