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NEET Sample Paper NEET Sample Test Paper-65

  • question_answer
    E, m, I and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of \[\frac{E{{l}^{2}}}{{{m}^{5}}{{G}^{2}}}\] are

    A) angle                

    B) length

    C) mass                            

    D) time

    Correct Answer: A

    Solution :

    \[[E]\,\,=\,\,[M{{L}^{2}}{{T}^{-2}}],\,\,[m]\,=\,[M],\,\,[l]\,\,=\,[M{{L}^{2}}{{T}^{-1}}]\,\] and \[~\left[ G \right]=\left[ {{M}^{-1}}\,{{L}^{3}}\,{{T}^{-}}^{2} \right]\] Substituting the dimension of above quantities in the given formula: \[\frac{E{{l}^{2}}}{{{m}^{5}}{{G}^{2}}}\,\,=\,\,\frac{[M{{L}^{2}}{{T}^{-2}}]\,{{[M{{L}^{2}}\,{{T}^{-1}}]}^{2}}}{[{{M}^{5}}]\,{{[{{M}^{-1}}\,{{L}^{3}}{{T}^{-2}}]}^{2}}}\] \[=\,\,\,\frac{{{M}^{3}}{{L}^{6}}{{T}^{-4}}}{{{M}^{3}}{{L}^{6}}{{T}^{-4}}}\,=\,\,[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]


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