The resultant force of a couple is ………?

1. Analyze the Question

The question asks for the resultant force of a "couple" in mechanics. A couple is a specific system of forces acting on a body.

2. Explain the Concept

In physics, a couple is defined as a pair of forces that are:

• Equal in magnitude.
• Parallel to each other.
• Acting in opposite directions.
• Separated by a perpendicular distance (the arm of the couple).

Because the two forces are equal and act in exactly opposite directions, they cancel each other out when you sum them up vectorially. However, they do not cancel out the turning effect (moment) of the forces; instead, they produce a rotation.

3. Show the Solution

Let the two forces be $F_1$ and $F_2$.

• By definition of a couple, $F_1 = F$ and $F_2 = -F$ (the negative sign indicates the opposite direction).

To find the resultant force ($F_R$), we add the forces together: $F_R = F_1 + F_2$ $F_R = F + (-F)$ $F_R = 0$

Since the resultant force is zero, a couple cannot cause a body to undergo linear acceleration; it can only cause the body to rotate about its center of mass.

4. Identify the Answer

The resultant force of a couple is always zero. Therefore, the correct option is B.

5. Exam Tip

Remember the "Couple Rule": Resultant Force = 0, but Resultant Moment $\neq$ 0. If you ever see a question about a couple, immediately think of a steering wheel—you push up with one hand and pull down with the other with equal force; the wheel doesn't move left or right (resultant force is zero), but it spins (moment is produced).