Question

For a body, angular velocity $\overrightarrow{\omega }=\hat{i}-2\hat{j}+3\hat{k}$ and radius vector $\overrightarrow{r}=\hat{i}+\hat{j}+\hat{k}$ , then its velocity is :-

• A. $-5\hat{i}+2\hat{j}+3\hat{k}$
• B. $-5\hat{i}+2\hat{j}-3\hat{k}$
• C. $-5\hat{i}-2\hat{j}+3\hat{k}$
• D. $-5\hat{i}-2\hat{j}-3\hat{k}$

Answer 1

The correct option is A $-5\hat{i}+2\hat{j}+3\hat{k}$

The velocity of a rotating body is given by:

$\overrightarrow{V}=\overrightarrow{\omega }$x$\overrightarrow{r}$

$\overrightarrow{V}=\left|\begin{array}{ccc}i& j& k\\ 1& -2& 3\\ 1& 1& 1\end{array}\right|$

$=\hat{i}(-2-3)-\hat{j}(1-3)+\hat{k}(1-(-2\left)\right)=-5\hat{i}+2\hat{j}+3\hat{k}$