Torque equilibrium about the hinge

Steps:

• Consider torques about hinge X for rotational equilibrium; net torque is zero.
• Torque due to weight: 10 N acts at midpoint (L/2 from X), so clockwise torque = 10 × (L/2) = 5L Nm.
• Torque due to F: vertical component F sin 30° acts upward at Y (distance L), so counterclockwise torque = (F × 0.5) × L = 0.5 F L Nm.
• Set torques equal: 0.5 F L = 5L → 0.5 F = 5 → F = 10 N.

Why C is correct:

• F = 10 N satisfies torque balance, as the vertical component (F sin 30°) provides exactly the torque needed to counter the weight's moment arm.

Why the others are wrong:

• A: Underestimates by halving F without considering the full torque equation.
• B: Likely misapplies cos 30° (≈0.866) to get ≈8.7 N, ignoring the vertical component.
• D: Assumes F equals weight directly, neglecting the 30° angle and lever arms.

Final answer: C