Net torque from perpendicular force components

Steps:

• Torque is force times perpendicular distance to line of action: τ = d × F × sinθ, where θ is angle between position vector and force.
• For F1, perpendicular component is F1 sinθ1; torque τ1 = d1 F1 sinθ1 (positive for opening direction).
• For F2, perpendicular component is F2 sinθ2; torque τ2 = -d2 F2 sinθ2 (negative if opposing rotational sense).
• Total moment = τ1 + τ2 = (d1 F1 sinθ1) - (d2 F2 sinθ2).

Why B is correct:

• Matches torque formula τ = r F sinθ, with subtraction for net effect when forces produce opposite rotations about hinge.

Why the others are wrong:

• A: Uses cosθ, giving parallel (not perpendicular) component, violating torque definition.
• C: Identical to B mathematically but omits parentheses, reducing clarity in expression.
• D: Uses addition with sinθ, ignoring opposing torque directions.

Final answer: B