Question

The linear velocity of a rotating body is given by $\overrightarrow{ v }=\vec{\omega} \times \overrightarrow{ r }$ . The angular velocity of body is $\vec{\omega}=5 \hat{ i }-4 \hat{ j }+9 \hat{ k }$ and the radius vector $\overrightarrow{ r }=8 \hat{ i }-6 \hat{ j }+3 \hat{ k }$ then $|\overrightarrow{ V }|$ is:

• A. $70.8\,$ units
• B. $90\,$ units
• C. $\sqrt{149}$ units
• D. $\sqrt{2017}$ units

Answer 1

Answer: (A)

As, $\overrightarrow{ V }=\vec{\omega} \times \overrightarrow{ r },$ then
$\vec{V}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{ k } \\ 5 & -4 & +9 \\ 8 & -6 & 3\end{array}\right|$
$\overrightarrow{ V }=\hat{ i }(-12-(-54)-\hat{ j }(15-72)+\hat{ k }(-30-(-32)))$
$\overrightarrow{ V }=42 \hat{ i }-57 \hat{ j }+2 \hat{ k }$
$|\overrightarrow{ V }|=\sqrt{(42)^{2}+(57)^{2}+(2)^{2}}$
$|\overrightarrow{ V }|=\sqrt{5017}=70.8\,$ unit