Question

A couple consists of

• A. Two like parallel forces of same magnitude
• B. Two like parallel forces of different magnitude.
• C. Two unlike parallel forces of same magnitude.
• D. Two unlike parallel forces of different magnitudes.

Hint:

The moment of a couple is a "free vector," meaning its rotational effect is the same about any reference point in the plane of the couple. Its magnitude is always the product of one of the forces and the distance between them (\(F \times d\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In rigid body mechanics, forces can cause both translation and rotation. A couple is a specific force system that produces pure rotation with no net translational force.

Step 2: Detailed Explanation:
Let us analyze the mechanical characteristics of a couple:

A couple is defined as a system of two parallel forces that are equal in magnitude, opposite in direction (unlike), and separated by a perpendicular distance (\(d\)).

Because the two forces (\(\vec{F}\) and \(-\vec{F}\)) are equal and opposite, their vector sum is zero: \[ \Sigma \vec{F} = \vec{F} + (-\vec{F}) = 0 \] This means a couple does not produce any net translational acceleration on a body.

However, because the two forces do not act along the same line of action, they produce a net moment (torque) about any point in their plane: \[ M = F \times d \] This moment causes pure rotational acceleration of the body.
Let us review the incorrect options:
-Like parallel forces act in the same direction, which results in a net translational force, so they cannot form a couple.
-Forces of different magnitudes do not cancel each other out, which would cause both translation and rotation.
Thus, only two unlike parallel forces of the same magnitude form a couple.

Step 3: Final Answer:
A couple consists of two unlike parallel forces of the same magnitude, which corresponds to Option (C).