Engineering mechanics – properties of a couple (pure moment) Which of the following statements correctly describe a force couple in statics and dynamics?

Introduction / Context:
A couple is a fundamental concept in engineering mechanics. It consists of two equal, parallel, and opposite forces separated by a distance, creating a pure moment with no net resultant force. This question checks your understanding of the defining properties and implications of a couple in equilibrium and motion analysis.

Given Data / Assumptions:

• Two forces are equal in magnitude, opposite in direction, and non-collinear.
• The perpendicular distance between their lines of action is constant.
• Rigid-body assumptions; forces are coplanar for simplicity.

Concept / Approach:
The net force of a couple is zero because forces cancel vectorially. However, they produce a moment M = F * d about any point. Since the resultant force is zero, the moment of a couple is free vector: its magnitude and sense are independent of the moment center. A single force cannot nullify a pure moment; only another couple of equal magnitude and opposite sense can.

Step-by-Step Solution:

Verification / Alternative check:
Replace a wrench (force + couple) by an equivalent system. Removing the force leaves a pure couple. To counter it, another couple of opposite sense is required; adding a single force reintroduces a resultant.

Why Other Options Are Wrong:

• Each of A, B, and C is correct individually; the best composite choice is “All of the above”.

Common Pitfalls:
Assuming the couple’s moment depends on the reference point. Unlike a force’s moment, a couple’s moment is invariant with respect to the moment center.

Final Answer:
All of the above