Moments from perpendicular force components about hinge P

Steps:

• Length PQ = 50 cm = 0.5 m.
• 5 N force is perpendicular to bar (diagram), moment = 5 N × 0.5 m = 2.5 Nm clockwise.
• 10 N force at angle θ to bar with sin θ = 0.2 (diagram), perpendicular component = 10 N × 0.2 = 2 N counterclockwise, moment = 2 N × 0.5 m = 1 Nm.
• Total moment = 2.5 Nm - 1 Nm = 1.5 Nm.

Why A is correct:

• Net perpendicular component is 3 N; moment = 3 N × 0.5 m = 1.5 Nm, using τ = r F⊥.

Why the others are wrong:

• B. 4.4 Nm: Adds components without subtracting opposing directions.
• C. 6.5 Nm: Assumes larger angle for 10 N force, overestimating its contribution.
• D. 9 Nm: Treats length as 0.9 m or ignores angles entirely.

Final answer: A