Question

Define moment of couple. Write its SI unit.

Answer 1

Hint : A couple is a system of forces with a resultant (a.k.a. net or sum) moment but no resultant force. So from the formula for a moment of a couple, we can find its SI unit.

Complete step by step answer
Moment refers to a very short period of time. If you consider a see-saw, putting weights on both sides makes it to be in a balanced moment. If you put extra weight or less weight, on one hand, the see-saw is no more balanced, and this is known as the unbalanced moment. The measure of turning effect is known as torque. The force which acts on the body of the torque is known as the moment of force.
Moment of force is a vector that is by definition is a cross product between radius (position vector) from the axes to the point of application of force, and force itself, but it is just a definition and we need to see beyond formulas if we want to know and understand physics and nature itself. Moment of force in rotational dynamics is the analogue of a force in classical non-rotational dynamics, and of force is a measure of how two objects interact and how much acceleration it will get, in rotational dynamics moment of force is how this body makes rotate and how much angular acceleration it will get so just understand the link between two and it will become easy.
The moment formula is given by
Moment of force = $ F \times d $
Where, $ F $ is the force applied and $ d $ is the distance from the fixed axis.
Moment of force is expressed in Newton meter (Nm).
Moment of force formula can be applied to calculate the moment of force for balanced as well as unbalanced forces.
In other words, moment of a force is basically, a quantity which represents the rotational effect caused by a force when applied to a body at any other point than its centre of gravity or its pivot point.
By Newton's third law, this force has an equal and opposite reaction at the point of pivot or its CG.
The SI unit of force is Newton, denoted by $ N $ and the unit of distance is $ m $ . Thus the SI unit of force is $ Nm $ .
Again, the unit of force is $ kg{m \mathord{\left/
 {\vphantom {m {{s^2}}}} \right.} {{s^2}}} $ and the unit of distance is $ m $ .
Thus the unit of Moment of Force is: $ kg{{{m^2}} \mathord{\left/
 {\vphantom {{{m^2}} {{s^2}}}} \right.} {{s^2}}} $ .

Note
Moment of force in two dimensional space is a scalar, only in 3D it becomes a vector. This is the same with the angular momentum and momentum, angular velocity and velocity, mass and moment of inertia etc.