Question

Find the torque about the origin when a force $3\hat{j}\text{N}$ acts on a particle whose position vector is $2\hat{k}\text{m}$.

• A. $-6\hat{i}\text{N-m}$
• B. $6\hat{k}\text{N-m}$
• C. $6\hat{i}\text{N-m}$
• D. $6\hat{j}\text{N-m}$

Answer 1

The correct option is A $-6\hat{i}\text{N-m}$

Torque around a point of rotation is given by the cross product of position vector and the force vector.

Position vector $\overrightarrow{r}$= $2\hat{k}\text{m}$
Force vector $\overrightarrow{F}$ = $3\hat{j}\text{N}$

Therefore
$\overrightarrow{\tau }$=$\overrightarrow{r}\times \overrightarrow{F}$
$\overrightarrow{\tau }=2\hat{k}\times 3\hat{j}$
$\overrightarrow{\tau }=-6\hat{i}$