Torque equilibrium about hinge Y

Steps:

• Rod at 60° to vertical wall means 30° to horizontal; weight acts at midpoint with lever arm (L/2) cos 30° = (L/2)(√3/2).
• Torque from weight = 3 × (L/2)(√3/2) = (3√3 L)/4 (one direction).
• Force F at 30° to rod gives perpendicular component F sin 30° = F/2; torque = (F/2) × L = FL/2 (opposite direction).
• Set torques equal for equilibrium: FL/2 = (3√3 L)/4; cancel L, F = (3√3)/2 N.

Why C is correct:

• Torque balance yields F = (3√3)/2 ≈ 2 N, per the principle of moments in static equilibrium.

Why the others are wrong:

• A. 0.87 N: Mistakenly uses sin 30° as lever arm for weight instead of cos 30°.
• B. 1.5 N: Assumes rod at 60° to horizontal, giving cos 60° = 0.5 in formula.
• D. 5 N: Omits halving distance to center of mass, yielding ≈ 3√3 N.

Final answer: C