Explanation:
When two coplanar couples have equal and opposite moments, they cannot balance each other. This means that the overall moment produced by the two couples will not be zero, and there will be a resulting moment or torque.

Definition of a Couple:
A couple is a pair of forces that are equal in magnitude, opposite in direction, and do not share the same line of action. These forces create a moment or torque that tends to rotate an object about an axis.

Balance of Couples:
When two couples have equal and opposite moments, they are said to be balanced. This means that the moments created by the two couples cancel each other out, resulting in a net moment of zero. In other words, the combined effect of the two couples is a null or balanced moment.

Equivalent Couples:
When two couples have equal and opposite moments, they are also considered to be equivalent. This means that the two couples have the same effect on an object in terms of rotation. Although the net moment produced by the two couples is zero, they individually produce a moment or torque.

Production of a Moment:
When two coplanar couples have equal and opposite moments, they do not balance each other and instead produce a moment or couple. The resulting moment is the vector sum of the moments produced by the two couples.

Example:
For example, consider two couples with moments of +10 Nm and -10 Nm, acting in the same plane. These two couples have equal and opposite moments, indicating a balanced or equivalent condition. However, they do not cancel each other out and instead produce a moment of 0 Nm.

Thus, the correct answer is option 'B' - two coplanar couples having equal and opposite moments cannot balance each other as they produce a moment or couple.