Question

The linear velocity of a 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 $\left|\begin{array}{c}\overrightarrow{v}\end{array}\right|$ is:

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

Answer 1

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

Here, $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}=(\hat{i}-2\hat{j}+2\hat{k})\times (4\hat{j}-3\hat{k})=-2\hat{i}+3\hat{j}+4\hat{k}$

Thus, $|\overrightarrow{v}|=\sqrt{(-2{)}^2+3^2+4^2}=\sqrt{29}$ units