Question 62009PhysicsWAEC

Which of the following types of motion will be produced when a pair of equal and opposite non-collinear parallel forces acts on a body?

A

Vibrational motion

B

Random motion

C

Translational motion

D

Rotational motion

Step-by-Step Explanation

A pair of equal and opposite non-collinear parallel forces forms a couple.

Let the two forces be FF and −F-F, acting along parallel but different lines of action.

Step 1: Consider the net force

Since the forces are equal in magnitude and opposite in direction,

Fnet=F+(−F)=0F_{\text{net}} = F + (-F) = 0

So there is no resultant force on the body.

Because the net force is zero, the body will not undergo translational motion due to these forces.

Step 2: Consider the turning effect

Although the net force is zero, the forces act along different lines of action. Since they are non-collinear, they produce a turning effect.

The moment of a couple is given by:

τ=Fd\tau = Fd

where:

  • τ\tau is the torque or moment of the couple,
  • FF is the magnitude of one of the forces,
  • dd is the perpendicular distance between the two lines of action.

Since F≠0F \neq 0 and d≠0d \neq 0,

τ≠0\tau \neq 0

So the forces produce a non-zero torque.

Step 3: Determine the type of motion

A non-zero torque causes a body to rotate. Therefore, the pair of equal and opposite non-collinear parallel forces produces rotational motion.

Hence, the correct answer is:

(D) Rotational motion

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