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NEET Sample Paper NEET Sample Test Paper-90

  • question_answer
    The linear velocity of a rotating body is given by \[\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}\] If \[\overrightarrow{\omega }=\overrightarrow{i}-2\hat{j}+2\hat{k}\] and \[\overrightarrow{r}=4\hat{j}-3\hat{k},\] then the magnitude of \[\overrightarrow{v}\] is

    A) \[\sqrt{29}\]units

    B) \[\sqrt{31}\] units

    C) \[\sqrt{37}\]units

    D)         \[\sqrt{37}\] units

    Correct Answer: A

    Solution :

    [a] \[\overrightarrow{v}=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    1 & -2 & 2  \\    0 & 4 & -3  \\ \end{matrix} \right|\] \[\overrightarrow{v}=\hat{i}[6-8]+\hat{j}[0+3]+\hat{k}[4-0]\] \[\overrightarrow{v}=-\,2\hat{i}+3\hat{j}+4\hat{k}\]\[\Rightarrow \]\[|\overrightarrow{v}|=\sqrt{29}\,\,units.\]


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