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

  • question_answer
    Two planets move around the sun. The periodic times and the mean radii of the orbits are \[{{T}_{1}},\,{{T}_{2}}\] and \[{{r}_{1}},\,{{r}_{2}}\] respectively. The ratio \[{{T}_{1}}/{{T}_{2}}\] is equal to                                    [CPMT 1978]

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

    B)               \[{{r}_{1}}/{{r}_{2}}\]

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

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

    Correct Answer: D

    Solution :

                    \[{{T}^{2}}\propto {{r}^{3}}\,\Rightarrow \,\frac{{{T}_{1}}}{{{T}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3/2}}\]


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