Torque of a couple equals force magnitude times separation distance

Steps:

• Recall torque τ for a couple: τ = F × d, where forces are equal in magnitude and opposite in direction.
• Calculate for equal-force options: A gives 30 N × 2 m = 60 Nm; D gives 15 N × 2 m = 30 Nm.
• Check unequal-force options: B (40 N, 10 N) and C (25 N, 5 N) cannot form a pure couple as forces differ.
• Verify match: Only D yields exactly 30 Nm.

Why D is correct:

• Equal forces of 15 N separated by 2 m give τ = 15 × 2 = 30 Nm, per couple torque formula.

Why the others are wrong:

• A: 30 N × 2 m = 60 Nm, twice the required torque.
• B: Unequal forces (40 N ≠ 10 N) do not form a couple; net force ≠ 0.
• C: Unequal forces (25 N ≠ 5 N) prevent pure couple formation.

Final answer: D