A pair of forces with equal magnitude, opposite directions, and different lines of action is called a "couple." When a couple acts on a rigid object, the couple produces a torque that does not depend on the location of the axis. The drawing shows a couple acting on a tire wrench, each force being perpendicular to the wrench. Determine an expression for the torque produced by the couple when the axis is perpendicular to the tire and passes through the following. Express your answers in terms of the magnitude F of the force and the length L of the wrench.

The drawing shows the couple acting on a tire wrench is missing and so i have attached it.

We are to find an expression for the torque when the axis is perpendicular to the tire and passes through the points A, B & C

Point A: τ = Fl

Point B: τ = 0

Point C: - Fl

Explanation:

Formula for torque is;

τ = F × d

Where;

F is perpendicular force

d is distance.

Thus;

> At point A, it means we are taking torque about point A and so we have;

τ = (-F × 0) + (F × L)

τ = Fl

> At point B, it means we are taking torque about point B and so we have;

τ = (-F × L/2) + (F × L/2)

τ = -(FL/2) + (FL/2)

τ = 0

> At point C, it means we are taking torque about point C and so we have;

τ = (-F × L) + (F × 0)

τ = -FL