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CMC Medical CMC-Medical Ludhiana Solved Paper-2013

  • question_answer
    Position of a body with acceleration \[a\] is given by \[x=k{{a}^{m}}\,{{t}^{n}},\] here \[t\] is time. Find the dimensions of \[m\] and \[n\]

    A)  \[m=1,\text{ }n=1\]     

    B)  \[m=1,\text{ }n=2\]

    C)  \[m=2,\text{ }n=1\]      

    D)  \[m=2,\text{ }n=2\]

    Correct Answer: B

    Solution :

                    Position \[x=k{{a}^{m}}{{t}^{n}}\] Writing the dimensions on both sides \[[{{M}^{0}}L{{T}^{0}}]={{[L{{T}^{-2}}]}^{m}}\,{{[T]}^{n}}\]   \[=[{{M}^{0}}{{L}^{m}}{{T}^{-2m+n}}]\] On comparing both sides \[m=1\] \[-\,2m+n=0\] \[n=2\,m\] \[=2\times 1=2\]


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