Definition of a Couple in Mechanics

Steps:

• Recall that a couple consists of two equal and opposite forces separated by a distance.
• Determine the net force: equal and opposite forces cancel, producing no resultant force.
• Determine the net moment: the forces create a torque equal to force times perpendicular distance, producing a resultant moment.
• Match this to the option describing no resultant force but a resultant moment.

Why B is correct:

• A couple is defined as two equal, parallel, opposite forces that produce no net force but a net torque (moment) about any point, per rigid body statics.

Why the others are wrong:

• A: Equal opposite forces along different lines do produce a moment, but the definition requires parallel lines for pure rotation.
• C: A couple always produces a resultant moment; no moment would mean equilibrium, not a couple.
• D: Unequal forces on the same line produce a net force, not a couple.

Final answer: B