Question

Moment of force $\left(\overrightarrow{F}\right)$ about an axis $\left(\overrightarrow{AB}\right)$ is zero when

• A. $\overrightarrow{F}||\overrightarrow{AB}$
• B. $\overrightarrow{F}$ intersects $\overrightarrow{AB}$
• C. $\overrightarrow{F}\perp \overrightarrow{AB}$
• D. Both (a) and (b)

Answer 1

The correct option is D Both (a) and (b)

Moment of force $\overrightarrow{F}$ about an axis $\overrightarrow{AB}$
= Torque of force $\overrightarrow{F}$ about an axis $\overrightarrow{AB}$

We know,
Torque $\left(\tau \right)=\overrightarrow{r}\times \overrightarrow{F}$
Torque about axis $\overrightarrow{AB}$ is component of $\overrightarrow{r}\times \overrightarrow{F}$ along $\overrightarrow{AB}$ which is zero.
Then $\overrightarrow{r}\times \overrightarrow{F}$ should be perpendicular to $\overrightarrow{AB}$.
As $\overrightarrow{r}\times \overrightarrow{F}$ is perpendicular to $\overrightarrow{F}$
$⟹\overrightarrow{F}$ should be parallel or intersecting $\overrightarrow{AB}$.
Also when force passes through the axis of rotation, torque about that axis will be zero.
$\therefore$ Both (a) and (b) are correct.