Torque from tension using perpendicular component

Steps:

• Position vector r from X to Y is 0.40 m horizontal.
• Force F = 15 N acts at Y at 30° to horizontal.
• Angle θ between r and F is 30°.
• Moment magnitude = r F sin θ = 0.40 × 15 × sin 30° = 0.40 × 15 × 0.5 = 3 Nm.

Why A is correct:

• The moment (torque) formula is τ = r F sin θ, where θ is the angle between the position vector r and force F, yielding the perpendicular component's effect.

Why the others are wrong:

• B: Uses cos 30° (≈0.866) instead of sin 30°, giving ≈5.2 Nm.
• C: Incorrectly applies full F to a 0.60 m lever arm or miscalculates sin θ.
• D: Might use horizontal component (15 cos 30°) times full r, giving ≈5.2 Nm, then doubled erroneously.

Final answer: A