Resultant of concurrent forces on a particle (engineering mechanics) A number of forces act simultaneously on a single particle of a rigid body. According to the principle of composition of concurrent forces, state whether they can be replaced by an equivalent single resultant force, and identify the correct statement.

Introduction / Context:When several forces act simultaneously on a single particle (i.e., their lines of action intersect at one point), their combined effect can be represented by a single resultant. This core idea underpins free-body diagrams, equilibrium checks, and vector reduction in engineering mechanics.

Given Data / Assumptions:

• All forces are concurrent at a single point (particle idealization).
• Rigid-body effects such as moments from offset forces are not present because lines of action meet at the particle.
• Standard vector algebra applies to force addition.

Concept / Approach:

The principle of composition states that two or more concurrent forces can be replaced by their vector sum. The result is a single force (resultant) whose magnitude and direction are obtained by vector addition, and whose line of action passes through the same point as the original forces.

Step-by-Step Solution:

Verification / Alternative check:

Graphical polygon-of-forces or parallelogram construction gives the same resultant as analytical components, confirming equivalence.

Why Other Options Are Wrong:

(b) contradicts vector composition; (c) centre of gravity is irrelevant for a particle problem; (d) a pure couple arises only from equal and opposite non-concurrent forces.

Common Pitfalls:

Confusing particle mechanics (concurrent forces) with rigid-body mechanics where non-concurrency introduces resultant force plus a couple.

Final Answer:

May be replaced by a single force acting at the particle (resultant exists).