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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    If the velocity of light c, gravitational constant G and Plancks constant h are chosen as fundamental units, the dimensions of length L in the new system is:

    A)  \[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\]                             

    B)  \[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\]

    C)         \[[{{h}^{1}}{{c}^{-3}}{{G}^{1}}]\]             

    D)         \[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]

    E)  

    Correct Answer: D

    Solution :

    Let \[L=[{{h}^{a}}{{c}^{b}}{{G}^{d}}]\] \[\therefore \]\[[{{L}^{}}]={{[M{{L}^{2}}{{T}^{-1}}]}^{a}}{{[L{{T}^{-1}}]}^{b}}{{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]}^{c}}\] \[\Rightarrow \]               \[a=\frac{1}{2},b=-\frac{3}{2},d=\frac{1}{2}\] Hence, \[L=[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]


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