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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Kepler's Laws of Planetary Motion

  • question_answer
    Two planets at mean distance \[{{d}_{1}}\] and \[{{d}_{2}}\] from the sun and their frequencies are n1 and n2 respectively then                                  [Kerala (Med.) 2002]

    A)             \[n_{1}^{2}d_{1}^{2}={{n}_{2}}d_{2}^{2}\]

    B)               \[n_{2}^{2}d_{2}^{3}=n_{1}^{2}d_{1}^{3}\]

    C)             \[{{n}_{1}}d_{1}^{2}={{n}_{2}}d_{2}^{2}\]

    D)               \[n_{1}^{2}{{d}_{1}}=n_{2}^{2}{{d}_{2}}\]

    Correct Answer: B

    Solution :

        \[\frac{{{T}^{2}}}{{{R}^{3}}}=\frac{{{T}^{2}}}{{{d}^{3}}}=\frac{1}{{{n}^{2}}{{d}^{3}}}=\]constant             \[\therefore \,\,\,n_{1}^{2}d_{1}^{3}=n_{2}^{2}d_{2}^{3}\]                                    [where n = frequency]


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