Two forces forming a couple are separated by a distance of 25cm. If one of the forces equals 40N, what is the moment of the couple?

Analyze the question A couple is a pair of equal and opposite parallel forces whose lines of action are separated by a perpendicular distance. We are asked for the moment (torque) of the couple.

Concept Moment of a couple = one of the forces × perpendicular distance between the forces

Moment = F × d

Because the forces in a couple are equal in magnitude, "one of the forces equals 40 N" means each force is 40 N.

Solution

• F = 40 N
• d = 25 cm = 0.25 m (always convert to metres to get Nm)

Moment = 40 × 0.25 = 10 Nm

Checking the options

• A (1000) and B (500) come from multiplying by 25 and by other wrong factors, ignoring the cm to m conversion.
• D (5 Nm) would be what you get if you wrongly used 20 N or 0.125 m.
• E (1.6 Nm) comes from 40 ÷ 25, dividing instead of multiplying.
• C (10 Nm) is correct.

Answer: C. 10 Nm

Tip: Whenever you see "cm" in a moment or torque question and the answer is in Nm, convert to metres first. Also remember that for a couple you use only ONE of the forces, not the sum of both (using 80 N would be a common trap).