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JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Critical Thinking

  • question_answer
    If the constant of gravitation \[(G)\], Planck's constant \[(h)\] and the velocity of light \[(c)\] be chosen as fundamental units. The dimension of the radius of gyration is             [AMU (Eng.) 1999]

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

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

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

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

    Correct Answer: A

    Solution :

                    Let radius of gyration \[[k]\propto {{[h]}^{x}}{{[c]}^{y}}{{[G]}^{z}}\] By substituting the dimension of\[[k]=[L]\], \[[h]=[M{{L}^{2}}{{T}^{-1}}],\,[c]=[L{{T}^{-1}}],\,[G]=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]and by comparing the power of both sides we can get \[x=1/2,\,y=-3/2,\,z=1/2\] So dimension of radius of gyration are \[{{[h]}^{1/2}}{{[c]}^{-3/2}}{{[G]}^{1/2}}\]


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