JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Mock Test - Units Dimenstions and Measurment

  • question_answer
    In a direct impact, loss in kinetic energy is given by \[\Delta K=\frac{M_{1}^{{}}M_{2}^{{}}}{2(M_{1}^{{}}+M_{2}^{{}})}.(V_{1}^{{}}-V_{2}^{{}})_{{}}^{2}(1-k_{{}}^{2})\] with usual notations (except k). The quantity k will have dimensional formula

    A) [\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-2}\]]                  

    B) [\[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-1}\]]

    C) [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}\]]       

    D) [\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}\]]

    Correct Answer: C

    Solution :

    [c] It is clear that k should be dimensionaless \[[1-{{k}^{2}}]={{M}^{0}}{{L}^{0}}{{T}^{0}}\] Hence, [k]=\[{{M}^{0}}{{L}^{0}}{{T}^{0}}\] Actually k is the coefficient of restitution,


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