JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Self Evaluation Test - Physical World, Units and Measurements

  • question_answer
      The period of a body under SHM is represented 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.

    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 :

    [a] \[T={{[M{{L}^{-1}}{{T}^{-2}}]}^{a}}{{[{{L}^{-3}}M]}^{b}}{{[M{{T}^{-2}}]}^{c}}\] \[\Rightarrow b+a+c=0,-a-3b=0,-2a-2c=1\] \[\Rightarrow \,\,a=-\frac{3}{2},b=\frac{1}{2},c=1\]


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