A driver turns a car's steering wheel of diameter 36 cm by applying two equal and opposite forces of 15 N, one at each side of the rim, tangential to the wheel and in opposite directions, forming a couple. What is the torque of this couple?

AS Level Physics 9702: Torque of a Couple on a Steering Wheel

Setting up the problem

A couple consists of two equal, opposite, parallel forces whose lines of action are separated by a perpendicular distance. Here, the two forces of $15\text{ N}$ act tangentially at diametrically opposite points on the wheel’s rim, so the perpendicular distance between their lines of action is the wheel’s full diameter, not its radius: $d = 36\text{ cm} = 0.36\text{ m}$

Calculating the torque

The torque of a couple is given by one force multiplied by the perpendicular distance between the forces. This formula already accounts for both forces acting together, so the result should not be doubled: $\text{torque} = F \times d = 15 \times 0.36$ $\text{torque} = 5.4\text{ N m}$

Why the other options are wrong

A ( $2.7\text{ N m}$ ): uses the radius ( $0.18\text{ m}$ ) instead of the diameter as the separation between the two forces.
C ( $10.8\text{ N m}$ ): incorrectly doubles the torque as $2Fd$ , from thinking both forces must be counted separately, when $Fd$ already represents the couple’s full turning effect.
D ( $41.7\text{ N m}$ ): comes from dividing the force by the distance ( $15\div0.36$ ) instead of multiplying them.

Final answer

Torque of the couple $= \boxed{5.4}\text{ N m}$ , option B.