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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    A force \[(2\,\widehat{i}\,-\,2\,\widehat{j}\,+\,3\,\widehat{j}+4\widehat{k})N\] is applied at a point. Whose is the place at position vector is\[r\to =(3\widehat{i}\,-\,2\widehat{j}+3\widehat{k}).\]. The torque about the origin point will be

    A)  \[-6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]

    B)  \[-17\,\widehat{i}\,+6\widehat{j}-13\,\widehat{k}\]

    C)  \[6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]  

    D)  \[\widehat{i}\,-6\widehat{j}-5\,\widehat{k}\]

    Correct Answer: D

    Solution :

     \[\tau =\overrightarrow{r}\times \overrightarrow{F}\] \[=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    3 & -2 & 3  \\    2 & -3 & 4  \\ \end{matrix} \right|\] \[=\hat{i}-6\hat{j}-5\hat{k}\]


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