The resultant force in a couple is

Analyze the question The question asks about the resultant force of a couple. A couple is a pair of forces that are equal in magnitude, opposite in direction, and act along different (parallel) lines of action.

Explain the concept

• A couple has two forces, F and −F.
• Because they are equal and opposite, their vector sum is zero, so a couple produces no translation.
• The forces act along different lines, so they do produce a turning effect (a moment or torque) equal to F × d, where d is the perpendicular distance between the forces.

Step-by-step solution

1. Let the two forces be F (one direction) and −F (opposite direction).
2. Resultant force = F + (−F) = 0.
3. The couple still rotates the body, because the moment is F × d, which is not zero.

Checking the options

• A. zero: correct, since the forces cancel as vectors.
• B. infinite: not possible.
• C. the sum of the forces: the vector sum is zero, so this does not give a nonzero value. It is not the right choice.
• D. the product of the forces: the product is not a resultant, and the turning effect is force × distance, not force × force.

Answer: A. zero

Tip: Remember "Couple = no push, only twist." The resultant force is zero, but the moment is F × d. Examples include turning a tap, a steering wheel, or a key in a lock, where you apply equal and opposite forces to produce rotation only.