Uttarakhand PMT Uttarakhand PMT Solved Paper-2007

  • question_answer
    In the relation V = \[V=\frac{\pi p{{r}^{4}}}{8\eta l}\] where the symbols have their usual meanings, the dimensions of V are

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

    B)  \[[{{M}^{0}}{{L}^{3}}{{T}^{-1}}]\]

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

    D)  \[[M{{L}^{3}}{{T}^{0}}]\]

    Correct Answer: B

    Solution :

     \[V=\frac{\pi {{\Pr }^{4}}}{8\eta l}\] Dimensions of \[V=\frac{[P][{{r}^{4}}]}{[\eta ](l)}\] \[=\frac{[M{{L}^{-1}}{{T}^{-2}}][{{L}^{4}}]}{[M{{L}^{-1}}{{T}^{-1}}][L]}\] \[=[{{M}^{0}}{{L}^{3}}{{T}^{-1}}]\]


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