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

  • question_answer
    A bus travels distance \[x_{1}^{{}}\]when accelerates from rest at constant rate\[a_{2}^{{}}\]for some time and after that travels a distance\[x_{2}^{{}}\]when decelerates at a constant rate \[a_{2}^{{}}\]to come to rest. A student established a relation \[x_{1}^{{}}+x_{2}^{{}}=\frac{a_{1}^{{}}a_{2}^{{}}t_{{}}^{2}}{2(a_{1}^{{}}+a_{2}^{{}})}\] Choose the correct option(s).

    A) The relation is dimensionally correct

    B) The relation is dimensionally incorrect

    C) The relation may be dimensionally correct

    D) None of the above

    Correct Answer: A

    Solution :

    [a] LHS=\[[{{x}_{1}}+{{x}_{2}}]=[{{x}_{1}}]=[{{x}_{2}}]=[{{M}^{0}}L{{T}^{0}}]\] RHS= \[\left[ \frac{{{a}_{1}}{{a}_{2}}{{t}^{2}}}{2({{a}_{1}}+2a)} \right]=\frac{[L{{T}^{-2}}][L{{T}^{-2}}][{{T}^{2}}]}{[L{{T}^{-2}}]}=[{{M}^{0}}L{{T}^{0}}]\] \[\because \] LHS=RHS According to homogeneity principle, equation is dimensionally correct. Hence, option [a] is correct.


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