NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    The period of a body under SHM i.e. presented by \[T={{P}^{a}}{{D}^{b}}{{S}^{c}}\]; where \[P\] is pressure, \[D\] is density and \[S\] is surface tension. The value of \[a,\,b\] and \[c\] are  [CPMT 1981]

    A)             \[-\frac{3}{2},\,\frac{1}{2},\,1\]       

    B)             \[-1,\,-2,\,3\]

    C)             \[\frac{1}{2},\,-\frac{3}{2},\,-\frac{1}{2}\] 

    D)             \[1,\,2,\,\frac{1}{3}\]

    Correct Answer: A

    Solution :

                                By substituting the dimension of each quantity we get \[T={{[M{{L}^{-1}}{{T}^{-2}}]}^{a}}{{[{{L}^{-3}}M]}^{b}}{{[M{{T}^{-2}}]}^{c}}\]             By solving we get a = ? 3/2, b = 1/2 and c = 1


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