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NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    If \[P\] represents radiation pressure, \[c\] represents speed of light and \[Q\] represents radiation energy striking a unit area per second, then non-zero integers \[x,\,y\] and \[z\] such that \[{{P}^{x}}{{Q}^{y}}{{c}^{z}}\] is dimensionless, are                                 [AFMC 1991; CBSE PMT 1992; CPMT 1981, 92; MP PMT 1992]

    A)             \[x=1,\,\,y=1,\,\,z=-1\]

    B)               \[x=1,\,y=-1,\,z=1\]

    C)             \[x=-1,\,y=1,\,z=1\]   

    D)             \[x=1,\,y=1,\,z=1\]

    Correct Answer: B

    Solution :

                                By substituting the dimension of given quantities \[{{[M{{L}^{-1}}{{T}^{-2}}]}^{x}}{{[M{{T}^{-3}}]}^{y}}{{[L{{T}^{-1}}]}^{z}}={{[MLT]}^{0}}\]             By comparing the power of M, L, T in both sides \[x+y=0\]               .....(i)             \[-x+z=0\]                   .....(ii)             \[-2x-3y-z=0\]              ?(iii) The only values of  \[x,\,y,\,z\] satisfying (i), (ii) and (iii) corresponds to   .


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