Which of the following motions will be produced by a pair of equal, opposite and non-collinear parallel forces acting on a body?

Analyze the question

We are asked what motion results when two forces are:

• equal in magnitude,
• opposite in direction,
• parallel but not along the same line (non-collinear).

Explain the concept

A pair of forces like this is called a couple.

• Because the forces are equal and opposite, the resultant force is zero. The body therefore has no net push in any direction, so there is no translational motion.
• Because the lines of action are different, the forces have a turning effect (moment) about the body's centre. The moment of a couple = force × perpendicular distance between the forces.

Solution

1. Net force: F + (−F) = 0, so no translation.
2. Net moment: F × d ≠ 0 (d is the perpendicular distance between the lines of action), so there is a turning effect.
3. A body with a net moment but no net force rotates about an axis.

Examples: turning a steering wheel with both hands, turning a tap, or turning a key. Each uses a couple.

Why the other options are wrong

• A, E (Oscillatory and Vibratory): these need a restoring force that repeats, which a constant couple does not provide.
• B (Random): there is nothing random about the effect of a couple.
• D (Translational): this needs a non-zero resultant force, but here it is zero.

Answer: C. Rotational

Exam tip: Remember it as "Couple = Turn". If the forces are equal and opposite and on the same line, the body is in equilibrium. If they are on different lines, the body rotates.