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NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
     Position of a body with acceleration 'a' is given by \[x=K{{a}^{m}}{{t}^{n}},\]here t is time. Find dimension of m and n?                                                                                         [Orissa JEE 2005]

    A)             \[m=1\], \[n=1\]

    B)               \[m=1,\ n=2\]

    C)             \[m=2,\ n=1\]

    D)               \[m=2,\ n=2\]

    Correct Answer: B

    Solution :

                    As \[x=K{{a}^{m}}\times {{t}^{n}}\]             \[\left[ {{M}^{0}}L{{T}^{0}} \right]={{\left[ L{{T}^{-2}} \right]}^{m}}{{\left[ T \right]}^{n}}=\left[ {{L}^{m}}{{T}^{-2m+n}} \right]\]             \[\therefore \] \[m=1\] and \[-2m+n=0\]Þ \[n=2\].


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