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NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    If energy \[(E)\], velocity \[(v)\]and force \[(F)\] be taken as fundamental quantity, then what are the dimensions of mass                                                                                                                [AMU 2000]

    A)             \[E{{v}^{2}}\]         

    B)             \[E{{v}^{-2}}\]

    C)             \[F{{v}^{-1}}\]        

    D)             \[F{{v}^{-2}}\]

    Correct Answer: B

    Solution :

                    Let \[m\propto {{E}^{x}}{{v}^{y}}{{F}^{z}}\]             By substituting the following dimensions :             \[[E]=[M{{L}^{2}}{{T}^{-2}}],\,[v]=[L{{T}^{-1}}],\,[F]=[ML{{T}^{-2}}]\]             and by equating the both sides \[x=1,\,y=-2,\,z=0\]. So \[[m]=[E{{v}^{-2}}]\]


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