Question

If the position vector of a particle is $\overrightarrow{r}=(3\hat{i}+4\hat{j})$ meter and its angular velocity is $\overrightarrow{\omega }=(\hat{j}+2\hat{k})$ rad/sec then its linear velocity is (in m/s)

• A. $(8\hat{i}-6\hat{j}+3\hat{k})$
• B. $(3\hat{i}+6\hat{j}+8\hat{k})$
• C. -$(3\hat{i}+6\hat{j}+6\hat{k})$
• D. $(6\hat{i}+8\hat{j}+3\hat{k})$

Answer 1

The correct option is A $(8\hat{i}-6\hat{j}+3\hat{k})$

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