Question

Given $\overrightarrow{F}=(4\hat{i}+10\hat{j})$ and $\overrightarrow{r}=(5\hat{i}-3\hat{j}).$ Then torque $\tau$ is :

• A. $-62\hat{j}$
• B. $62\hat{k}$
• C. $48\hat{i}$
• D. $-48\hat{k}$

Answer 1

Answer: (B)

$62\hat{k}$

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

$=(5\hat{i}-3\hat{j})\times (4\hat{i}+10\hat{j})$
$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 5& -3& 0\\ 4& 10& 0\end{array}\right|$
$=\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}[+50-(-12\left)\right]$
$=62\hat{k}$