Question

Which of the following is/are the properties of a couple?
(This question has multiple correct options)
A. It tends to produce pure rotation
B. It is different about any point in the plane of lines of action of the forces.
C. It can be replaced by any other couple of the same moment
D. The resultant set of two or more couples is equal to the sum of the moments of the individual couples.

Answer 1

Hint: Couple is a pair of parallel forces of equal magnitude and opposite in directions. A couple generates a torque called the moment of couple. The torque is equal to the product of the force and the perpendicular distance between the forces. The net force is zero.

Complete step by step answer:
Let us first understand what is meant by a couple. Couple is a pair of parallel forces such that the magnitudes of these two forces are equal and both are opposite in the directions. A figure of a couple is given below.

When a couple acts on a body, it generates a torque on the body called the moment of the couple.
Consider a planar body. Suppose a couple acts on the body along the plane surface of the body. Let the magnitude of the forces be F and the perpendicular distance be d.

Since the two forces have equal magnitudes and are in opposite directions, the net force on the body is zero. Hence, the body will not have a translation motion. And we already know that the couple produces a torque on the body. This means that the body has a pure rotational motion.
Therefore, the moment of a couple tends to produce a pure rotational motion.
Hence, option A is correct.
Since the moment of a couple is a torque, it can be replaced by any other couple of the same moment.
Hence, option C is correct.
When two torques are acting on a body, the total torque on the body is equal to the sum of the individual torques.
The resultant set of two or more couples is equal to the sum of the moments of the individual couples.
Hence, the correct option is D.

Therefore, the correct option are A, C and D.

Note:
Let us discuss why option B is incorrect.
It talks about the moment (torque) about any point the plane of lines of action of the forces. The torque on genearted is equal to the product of the force (F) and the perpendicular distance between them (d). i.e. $\tau =Fd$.
This value of torque is constant about every point in the plane. Therefore, the moment of the couple is the same at any point in the plane of lines of action of the forces. Hence, option B is incorrect.