Torque of a Couple: Force Times Perpendicular Separation

Steps:

• Recognize the couple as two equal, opposite forces F applied parallel to each other on the tap.
• From the diagram, the perpendicular distance between the lines of action of the forces is 2d.
• Apply the formula for torque of a couple: τ = F × (perpendicular distance).
• Compute τ = F × 2d = 2Fd.

Why C is correct:

• The torque of a couple equals one force times the perpendicular distance between the forces' lines of action, which is 2d here, yielding 2Fd.

Why the others are wrong:

• A: Assumes separation of d/2, underestimating the actual 2d distance.
• B: Assumes separation of d, but the diagram shows 2d.
• D: Assumes separation of 4d, overstating the distance.

Final answer: C