Physics - Rotation Question with Solution | TestHub

A couple consists of two equal and opposite forces whose lines of action do not coincide. Since the net force is zero, a couple does not produce translational acceleration and cannot be balanced by a single force.

Let the forces be $\vec{F}$ applied at position ${\vec{r}}_1$ and $-\vec{F}$ applied at position ${\vec{r}}_2$. The total moment (torque) about an arbitrary origin is given by:

$\vec{\tau }={\vec{r}}_1\times \vec{F}+{\vec{r}}_2\times (-\vec{F})=({\vec{r}}_1-{\vec{r}}_2)\times \vec{F}$

The term $({\vec{r}}_1-{\vec{r}}_2)$ represents the relative position vector between the points of application on the two lines of action. This shows that the moment of a couple depends only on the perpendicular distance between the lines of action and the magnitude of the forces. It is entirely independent of the choice of the origin (axis of rotation). Furthermore, by the principle of transmissibility, the moment remains unchanged regardless of the specific points of application chosen along the respective lines of action.

Therefore, the moment of a couple is independent of the axis of rotation or the points of application of forces.

Answer: a