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Manipal Engineering Manipal Engineering 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 dimension of\[m\]and\[n\]

    A) \[m=1,\,\,n=1\]                               

    B) \[m=1,\,\,n=2\]

    C) \[m=2,\,\,n=1\]               

    D)        \[m=2,\,\,n=2\]

    Correct Answer: B

    Solution :

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


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