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

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$\sqrt{29} units$

$\sqrt{37} units$

$\sqrt{41} units$

$\sqrt{31} units$

answer is A.

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Detailed Solution

$\vec{v} = \vec{ω} \times \vec{r} = (\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 2 \\ 0 & 4 & - 3 \end{matrix})$

= $\hat{i} (6 - 8) - j (- 3) + 4 \hat{k} = - 2 \hat{i} + 3 \hat{j} + 4 \hat{k}$

$| \vec{v} | = \sqrt{{(- 2)}^{2} + {(3)}^{2} + 4^{2}} = \sqrt{29} unit$

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