Question

The condition for the equilibrium of a particle in a plane subjected to concurrent forces requires that:

• A. The sum of the forces in any one direction is zero
• B. The sum of the vertical forces equals the sum of the horizontal forces
• C. The algebraic sum of the moments about any point is zero
• D. The vector sum of all forces acting on the particle is zero

Hint:

For equilibrium of a particle, always ensure that the vector sum of all acting forces is zero: \( \sum \vec{F} = 0 \). Moment equilibrium applies only to extended bodies, not to point particles.

Answer 1

The Correct Option is D

Step 1: For a particle to be in equilibrium under the action of concurrent forces, the net force acting on it must be zero. This is a direct consequence of Newton’s First Law of Motion.
Step 2: Mathematically, this means the vector sum of all forces acting on the particle must vanish: \[ \sum \vec{F} = 0 \] This ensures that there is no acceleration and the particle remains at rest or continues in uniform motion.
Step 3: Since the forces are concurrent (acting through a common point), there is no net torque or moment about any point, and we only need to consider the force balance.
Why the other options are incorrect:

• (A) Force balance must be satisfied in both horizontal and vertical directions, not just in one direction.
• (B) Equal magnitudes of vertical and horizontal forces do not guarantee zero net force unless their directions cancel out vectorially.
• (C) Moment equilibrium is essential for rigid bodies but is not a condition for a particle under concurrent forces.