Definition of a couple in planar mechanics Two equal and opposite parallel forces whose lines of action are different form a couple. Assess the statement.

Introduction / Context:Couples are essential in statics because they create pure rotation without net translation. Recognizing when forces constitute a couple is a core skill.

Given Data / Assumptions:

• Two forces F and −F, parallel, separated by a perpendicular distance d.
• Lines of action do not coincide (nonzero arm).

Concept / Approach:A couple is a free vector characterized by its moment M = F * d (about any point). The net force is zero (equal and opposite), but the net moment is nonzero because of the arm between the forces.

Step-by-Step Solution:

Verification / Alternative check:Shift the reference point; a couple’s moment is invariant with respect to the choice of origin (free vector property), confirming the identification.

Why Other Options Are Wrong:

• “Incorrect” would imply either unequal magnitudes or coincident lines of action; the statement explicitly rules those out.

Common Pitfalls:Confusing a couple with a single force pair where lines of action coincide (which would cancel with no moment).

Final Answer:Correct