Question

The SI unit of moments of couple is _____.
A. \[{{{N}}^{{2}}}\,{{m}}\]
B. \[{{N}}\,{{m}}\]
C. \[{{N}}\,{{{m}}^{{2}}}\]
D. \[{{N/}}{{{m}}^{{2}}}\]

Answer 1

Hint: By multiplying the magnitude of one of the forces \[\left( F \right)\] by the perpendicular distance between the two forces \[\left( s \right)\], the moment (or torque) of a couple is determined. The SI unit of force is Newton and that of the distance is metres.

Complete answer:
In the given question, we are asked about the SI unit of moment. First of all, we will find out which are the physical quantities that constitute the moment of a couple.
Couple is defined as the action of equal and opposite parallel forces acting on two distinct axes. The pair have the same SI unit as the torque unit.
Torque is the moment of a couple that is equal to the force product applied to the distance. The SI unit is \[{\text{Nm}}\].
A couple moment is a free vector. The moment of the couple acts at any point in space, since moment depends only on the position vector which is directed in between the forces.
Mathematically, we can write:
\[\vec M = \vec r \times \vec F\]
where,
Unit of \[\vec F\] is Newton.
Unit of \[\vec r\] is metre.
Hence, the SI unit is \[{\text{Nm}}\].

The correct option is option B.

Note:
A special case is a couple of moments. There are two opposing forces in a pair that are similar in size, opposite in context and do not share a line of action. It generates no translation whatsoever, just rotation. A couple's subsequent power is zero. But, zero is not the product of a couple; it's a single moment.