Torque of a Couple

Steps:

• Identify the setup: two equal forces F act in opposite directions, each at distance d from pivot P, forming a couple with separation 2d.
• Calculate torque from first force: magnitude F × d, direction clockwise (assuming positions).
• Calculate torque from second force: magnitude F × d, direction also clockwise due to opposite force direction on the other side.
• Add torques: net torque = F d + F d = 2 F d.

Why C is correct:

• By definition, torque of a couple equals force times perpendicular distance between lines of action (2d), so F × 2d = 2 F d.

Why the others are wrong:

• A: Ignores rotational effect; forces do not cancel torques about P.
• B: Accounts for only one force's torque, missing the second.
• D: Incorrectly squares F, violating torque formula τ = r F sinθ.

Final answer: C