Torque from weight at center of mass

Steps:

• Center of mass is at midpoint of sign, distance L/2 = 0.26 m from hinge along tilted plane.
• Horizontal distance from hinge to center of mass: d = (L/2) sin(25°) = 0.26 × 0.4226 ≈ 0.110 m.
• Weight force: mg = 36 kg × 9.8 m/s² = 352.8 N.
• Moment (torque) = mg × d = 352.8 × 0.110 ≈ 38.8 Nm, which rounds to 38 Nm.

Why A is correct:

• Torque equals force times perpendicular distance from pivot to line of action; for vertical weight, this is the horizontal offset to center of mass, per basic mechanics definition.

Why the others are wrong:

• B: Uses full side length L instead of L/2 for distance to center, giving mg × (L sin 25°) ≈ 78 Nm.
• C: Likely miscalculates sin(25°) or g value, overestimating perpendicular distance.
• D: Ignores tilt by using full vertical distance L/2 without sin(25°), giving mg × (L/2) ≈ 92 Nm.

Final answer: A