Question

If $\overline{F}=2\overline{i}-3\overline{j}$ $N$ and $\overline{r}=3\overline{i}+2\overline{j}$ $m$. The torque $\tau$ is:

• A. $12\hat{k}$
• B. $13\hat{k}$
• C. $-12\hat{k}$
• D. $-13\hat{k}$

Answer 1

Answer: (D)

$-13\hat{k}$

$\tau =\overrightarrow{r}\times \overrightarrow{F}$
$=(3\overline{i}+2\overline{j})\times (2\overline{i}-3\overline{j})$
$=(3\times 2)(\overline{i}\times \overline{i})-3\times 3(\overline{i}\times \overline{j})+(2\times 2)(\overline{j}\times \overline{i})-2\times 3(\overline{j}\times \overline{j})$
$=-(3\times 3)\overline{k}-4\overline{k}$
$=-13\overline{k}$