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BCECE Medical BCECE Medical Solved Papers-2012

  • question_answer
    Two planets revolves around the sun with frequencies \[{{N}_{1}}\] and \[{{N}_{2}}\] revolutions per year. If their average radii (orbital) be \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively, then \[{{R}_{1}}/{{R}_{2}}\] is equal to

    A)  \[{{({{N}_{1}}/{{N}_{2}})}^{2/3}}\]

    B)  \[{{({{N}_{1}}/{{N}_{2}})}^{3/2}}\]

    C)  \[{{({{N}_{2}}/{{N}_{1}})}^{2/3}}\]

    D)  \[{{({{N}_{2}}/{{N}_{1}})}^{3/2}}\]

    Correct Answer: C

    Solution :

    According to Keplers law of planetary motion                 \[{{T}^{2}}\propto {{R}^{3}}\] If N is the frequency then                 \[{{N}^{2}}\propto {{(R)}^{-3}}\] or            \[\frac{{{N}_{2}}}{{{N}_{1}}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{-3/2}}\] \[\Rightarrow \] \[\frac{{{R}_{1}}}{{{R}_{2}}}={{\left( \frac{{{N}_{2}}}{{{N}_{1}}} \right)}^{2/3}}\]


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