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NEET Sample Paper NEET Sample Test Paper-88

  • question_answer
    The position x of a particle at time t is given by\[x=\frac{{{V}_{0}}}{a}(1-{{e}^{-at}},)\] where \[{{V}_{0}}\] is constant and \[a>0.\] The dimensions of \[{{V}_{0}}\] and a are respectively

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

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

    C) \[{{M}^{0}}L\,{{T}^{-1}}\] and \[L{{T}^{-2}}\]

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

    Correct Answer: A

    Solution :

    [a] Here, at is dimensionless \[\Rightarrow \]\[a=\frac{1}{t}=\left[ \frac{1}{T} \right]=\left[ {{T}^{-1}} \right]\] \[x=\frac{{{V}_{0}}}{a}\] and \[{{V}_{0}}=xa=\left[ L{{T}^{-1}} \right]=\left[ {{M}^{0}}L{{T}^{-1}} \right]\]


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