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NEET Sample Paper NEET Sample Test Paper-10

  • question_answer
    Energy due to position of a particles is given, \[U=\frac{\alpha \sqrt{V}}{Y+\beta },\] where \[\alpha \] and \[\beta \] are constants, Y is distance. The dimensions of \[(\alpha \times \beta )\] are

    A)  \[[{{M}^{3}}L{{T}^{0}}]\]                    

    B)  \[[{{M}^{1/2}}{{L}^{3/2}}{{T}^{-2}}]\]

    C)  \[[{{M}^{0}}{{L}^{-7/2}}{{T}^{0}}]\]          

    D)  \[[M{{L}^{7/2}}{{T}^{-2}}]\]

    Correct Answer: B

    Solution :

    \[[\beta ]=L\] \[[M{{L}^{2}}{{T}^{-2}}]=\frac{\alpha {{[L]}^{1/2}}}{[L]}\] \[\alpha =[M]\,[{{L}^{5/2}}]\,[{{T}^{-2}}]\] \[\Rightarrow \] dimensions of \[(\alpha \times \beta )=[M{{L}^{5/2}}{{T}^{-2}}]\times (L)\]                                 \[=[M{{L}^{7/2}}{{T}^{-2}}]\]


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