Question

The velocity of the rotating body is given by $\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r},$ where $\overrightarrow{\omega }$ is the angular velocity and $\overrightarrow{r}$ is the radius vector. The angular velocity of a body is $\overrightarrow{\omega }=\hat{i}-2\hat{j}+2\hat{k}$ and the radius vector $\overrightarrow{r}=4\hat{j}-3\hat{k},$ then $|\overrightarrow{V}|$ is

• A. $\sqrt{29}$
• B. $\sqrt{31}$
• C. $\sqrt{37}$
• D. $\sqrt{41}$

Answer 1

The correct option is A $\sqrt{29}$

$\overrightarrow{V}=\overrightarrow{\omega }\times \overrightarrow{r}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -2& 2\\ 0& 4& -3\end{array}\right|=\hat{i}(6-8)-\hat{j}(-3)+4\hat{k}$
$\overrightarrow{V}=-2\hat{i}+3\hat{j}+4\hat{k}$
$|\overrightarrow{V}|=\sqrt{(-2{)}^2+3^2+4^2}$
$=\sqrt{29}$