NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    The equation of state of some gases can be expressed as \[\left( P+\frac{a}{{{V}^{2}}} \right)\,(V-b)=RT\]. Here \[P\] is the pressure, \[V\] is the volume, \[T\] is the absolute temperature and \[a,\,b,\,R\] are constants. The dimensions of \['a'\] are [CBSE PMT 1991, 96; NCERT 1984; MP PET 1992; CPMT 1974, 79, 87, 97; MP PMT 1992, 94; MNR 1995; AFMC 1995]

    A)             \[M{{L}^{5}}{{T}^{-2}}\]          

    B)             \[M{{L}^{-1}}{{T}^{-2}}\]

    C)             \[{{M}^{0}}{{L}^{3}}{{T}^{0}}\]      

    D)             \[{{M}^{0}}{{L}^{6}}{{T}^{0}}\]

    Correct Answer: A

    Solution :

                    By principle of dimensional homogenity \[\left[ \frac{a}{{{V}^{2}}} \right]=\left[ P \right]\] \[\therefore \] \[[a]=[P]\ [{{V}^{2}}]=[M{{L}^{-1}}{{T}^{-2}}]\ \times [{{L}^{6}}]\]  = \[[M{{L}^{5}}{{T}^{-2}}]\]


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