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BHU PMT BHU PMT (Mains) Solved Paper-2007

  • question_answer
    A hypothetical experiment conducted to determine Young s formula\[Y=\frac{\cos \,\theta \,{{T}^{x}}.\tau }{{{l}^{3}}}\]. If Y = Young's  modulus, T = time  period, \[\tau =\]torque and\[l=\]length, then find the value of\[x\].

    A)  zero                                     

    B)  1

    C)  2                                            

    D)  3

    Correct Answer: A

    Solution :

                     We have, \[Y=\frac{\cos \theta {{T}^{x}}.\tau }{{{l}^{3}}}\]                               ?? (i) We know,           \[[Y]=[M{{L}^{-1}}{{T}^{-2}}],[T]=[{{T}^{1}}]\]                 \[[\tau ]=[M{{L}^{2}}{{T}^{-2}}]\] \[\theta =\]dimensionless                                 \[[l]=[L]\] Thus, Eq. (i) becomes                 \[[M{{L}^{-1}}{{T}^{-2}}]=\frac{{{[{{T}^{1}}]}^{x}}[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{3}}]}\] or            \[[M{{L}^{-1}}{{T}^{-2}}]=[M{{L}^{-1}}{{T}^{-2+x}}]\] Comparing the powers, we have \[-2+x=-2\] \[\therefore \]  \[x=0\]


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