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BCECE Engineering BCECE Engineering Solved Paper-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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