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NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    If the velocity of light \[(c)\], gravitational constant \[(G)\] and Planck's constant \[(h)\] are chosen as fundamental units, then the dimensions of mass in new system is                                        [UPSEAT 2002]

    A)             \[{{c}^{1/2}}{{G}^{1/2}}{{h}^{1/2}}\]          

    B)             \[{{c}^{1/2}}{{G}^{1/2}}{{h}^{-1/2}}\]

    C)             \[{{c}^{1/2}}{{G}^{-1/2}}{{h}^{1/2}}\]

    D)             \[{{c}^{-1/2}}{{G}^{1/2}}{{h}^{1/2}}\]

    Correct Answer: C

    Solution :

                    Let \[m\propto {{C}^{x}}{{G}^{y}}{{h}^{z}}\]             By substituting the following dimensions:             \[[C]=L{{T}^{-1}};\,[G]=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\] and \[[h]=[M{{L}^{2}}{{T}^{-1}}]\]             Now comparing both sides we will get             \[x=1/2;\,y=-1/2,\,z=+1/2\] So \[m\propto {{c}^{1/2}}{{G}^{-1/2}}{{h}^{1/2}}\]


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