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  • If  <img alt="\vec{w}=\hat{l}-2\hat{j}+2\hat{k}\; \; and\; \; \vec{r}=4\hat{j}-3\hat{k}," src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7Bw%7D%3D%5Chat%7Bl%7D-2%5Chat%7Bj%7D&p

If  \vec{w}=\hat{l}-2\hat{j}+2\hat{k}\; \; and\; \; \vec{r}=4\hat{j}-3\hat{k},  then the magnitude of \vec{V} is where V is the linear velocity, w is angular velocity and r is the radius vector

and \vec{V}  is given by (\vec{V}=\vec{ \omega }\times \vec{r })

Option: 1

\sqrt{29} \; \; units


Option: 2

\sqrt{31} \; \; units


Option: 3

\sqrt{37} \; \; units


Option: 4

\sqrt{41} \; \; units


Answers (1)

best_answer

Solution

Vector or cross product -

 \\*\vec{V}=\vec{\omega}\times \vec{r}\\*\\*\left | \vec{V} \right |=\left |\vec{\omega}\times \vec{r} \right |  

=\begin{Vmatrix} \hat{l} &\hat{j} &\hat{k} \\ 1&-2 &2 \\ 0 & 4 & -3 \end{Vmatrix}=\left | [\hat{l}(6-8)-\hat{j}(-3-0)+\hat{k}(4-0)] \right |

=\left | -2\hat{l}+3\hat{j}+4\hat{k} \right |=\sqrt{4+9+16}=\sqrt{29}\; unit

 

Posted by

Divya Prakash Singh

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