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?
Vibrational motion
Random motion
Translational motion
Rotational motion
Step-by-Step Explanation
A pair of equal and opposite non-collinear parallel forces forms a couple.
Let the two forces be F and −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)=0So 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=Fdwhere:
- τ is the torque or moment of the couple,
- F is the magnitude of one of the forces,
- d is the perpendicular distance between the two lines of action.
Since F=0 and d=0,
τ=0So 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