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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    The position of a particle at time (t) is given by \[x(t)=({{v}_{0}}/\alpha )(1-{{e}^{-\alpha t}})\]. Here v0 and\[\alpha \]are constants and\[a>0\]. The dimension of v0 and \[\alpha \] are

    A)  \[\left[ {{M}^{0}}L{{T}^{-1}} \right]\]and\[\left[ L{{T}^{-1}} \right]\]

    B)  \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\left[ {{T}^{-1}} \right]\]  

    C)  \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\,\left[ T \right]\]

    D)  \[\left[ {{M}^{0}}L{{T}^{0}} \right]and\,\left[ {{T}^{-1}} \right]\]

    Correct Answer: B

    Solution :

     Dimension of\[\left[ \frac{{{v}_{0}}}{\alpha } \right]=\] Dimension of \[x\] and dimension of \[\alpha =\frac{1}{Dimension\,of\,t}\] \[=\frac{1}{[T]}\] \[=[{{T}^{-1}}]\] Dimensions of\[{{v}_{0}}=[{{M}^{0}}L{{T}^{-1}}]\]


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