Question

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

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

Answer 1

Answer: (A)

$\sqrt{29}$units

Answer 2

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

$- 2\overrightarrow{i} + 3\overrightarrow{j} + 4\overrightarrow{k}$

$|\overrightarrow{v}|\mspace{6mu} = \mspace{6mu}\sqrt{( - 2)^{2} + (3)^{2} + 4^{2}} = \sqrt{29}\mspace{6mu} unit$