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

  • question_answer
    The wavelength associated with a moving particle depends upon \[{{p}^{th}}\]power of its mass m, \[{{q}^{th}}\]power of its velocity v and \[{{r}^{th}}\] power of Planck's constant h. Then the sum of values of \[p\], q and r is -K. Find the value of K7.

    A) 2

    B) 4

    C) 5

    D) 1

    Correct Answer: D

    Solution :

    [1] Given \[\lambda =k{{m}^{p}}{{v}^{q}}{{h}^{k}}\]. The dimensions of right-hand rule and left-hand side terms should be equal. So \[[{{M}^{0}}L{{T}^{0}}]={{[M]}^{p}}{{[L{{T}^{-1}}]}^{q}}{{[M{{L}^{2}}{{T}^{-1}}]}^{r}}\] Or \[[{{M}^{0}}L{{T}^{0}}]=[{{M}^{p+r}}][{{L}^{q+2r}}][{{T}^{-q-r}}]\] Now , compare powers of M, L and T, we get p+r=0                          ...(i) q+2r=1            ...(ii) -q-r=0                           ...(iii) After solving p=-1, q=-1 and r=1 putting these values, we get


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