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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Critical Thinking

  • question_answer
    Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to \[{{R}^{-\frac{5}{2}}}\], then \[{{T}^{2}}\] is proportional to            [IIT 1989; RPMT 1997]

    A)             \[{{R}^{3}}\]

    B)                      \[{{R}^{7/2}}\]

    C)             \[{{R}^{5/2}}\]       

    D)             \[{{R}^{3/2}}\]

    Correct Answer: B

    Solution :

                    For revolution of planet centripetal force is provided by gravitational force of attraction             \[m{{\omega }^{2}}R\propto {{R}^{-5/2}}\]Þ\[\frac{1}{{{T}^{2}}}\propto {{R}^{-7/2}}\]\[\Rightarrow {{T}^{2}}\propto {{R}^{7/2}}\]


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