JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Self Evaluation Test - Physical World, Units and Measurements

  • question_answer
    Write the dimensions of \[a\times b\]in the relation \[E=\frac{b-{{x}^{2}}}{at}\]where E is the energy, x is the displacement and t is time

    A)  \[M{{L}^{2}}T\] 

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

    C)  \[M{{L}^{2}}{{T}^{-2}}\]

    D)  \[ML{{T}^{-2}}\]

    Correct Answer: B

    Solution :

    [b] Here, b and \[{{x}^{2}}={{L}^{2}}\]have same dimensions Also, \[a=\frac{{{x}^{2}}}{E\times t}=\frac{{{L}^{2}}}{(M{{L}^{2}}{{T}^{-2}})T}={{M}^{-1}}{{T}^{1}}\] \[a\times b=[{{M}^{-1}}{{L}^{2}}{{T}^{1}}]\]


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