Question

if force $\overrightarrow{F}=(\hat{i}+3\hat{j})N$ acts on a body at a point whose distance from the axis of rotation is given by $\overrightarrow{r}=(3\hat{i}+\hat{j})N$ then torque acting on the body is:

• A. $9Nm$
• B. $8Nm$
• C. $6Nm$
• D. $1Nm$

Answer 1

The correct option is B $8Nm$

We know that

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{7}$

$\overrightarrow{r}=3\hat{i}+\hat{j}$ and $\overrightarrow{7}=\hat{i}+3\hat{j}$

$\overrightarrow{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 1& 0\\ 1& 3& 0\end{array}\right|=(1\times 0-3\times 0)\hat{i}+(1\times 0-3\times 0)\hat{j}+(3\times 2-1\times 1)\hat{k}$

$\overrightarrow{\tau }=8\hat{k}$

$|\overrightarrow{\tau }|=|8\hat{k}|=8Nm$

Option $-B$ is correct.