Question

At a point $(2m,2m)$ a force of $10N$ is acting along positive z-direction. Torque of this force about x-axis will be

• A. $10\text{Nm}$
• B. $20\sqrt{2}\mathrm{Nm}$
• C. $10\sqrt{2}\mathrm{Nm}$
• D. $20\text{Nm}$

Answer 1

The correct option is D $20\text{Nm}$

By the definition of torque,
$\tau =r\times F$

Given point is $(2m,2m)=(2m,2m,0)$
Hence $\overrightarrow{r}=\left(2m\right)\hat{i}+\left(2m\right)\hat{j}+\left(0\right)\hat{k}$

Given that the force is acting along z-direction
Hence $F=10\hat{k}$

$\tau =\left(\right(2m)\hat{i}+(2m)\hat{j}+(0\left)\hat{k}\right)\times 10\hat{k}$

$\tau =20\hat{i}-20\hat{j}$
Thus, torque about x-axis is $20\text{Nm}$