Question

$AB,CD,EG$ are perpendicular to each other. Select the correct statement(s) :

• A. Torque about the axis $EG$ is $0$
• B. Torque about the axis $GH$ is $0$
• C. Torque about the axis $AB$ is $(OG\times F)$
• D. Torque about the axis $CD$ is $(OG\times F)$

Answer 1

Answer: (A), (B), (D)

Torque about the axis $CD$ is $(OG\times F)$

As we know
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
$\overrightarrow{\tau }=rF\sin \theta$

(a) Torque about axis $EG$ is zero, because the line of action of $F$ (force) intersects the line $EG$.

(b) Torque about axis $GH$ will be zero because the line of action of $F$ (force) is along the axis $GH$.

(c) Torque about axis $AB$ will be zero because $\overrightarrow{F}$ is parallel to axis $AB$.
$\overrightarrow{\tau }=rF\sin \theta$ and $\theta =0$
Hence, $\overrightarrow{\tau }=0$

(d) Torque about axis $CD$ will be $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
$\overrightarrow{\tau }=(\overrightarrow{OG}\times \overrightarrow{F})$
Hence $A,B,D$ statements are correct.