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

  • question_answer
     Suppose the gravitational force varies inversely as the \[{{n}^{th}}\] power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to                                         [AIEEE 2004]

    A)                 \[{{R}^{\left( \frac{n+1}{2} \right)}}\]           

    B)                 \[{{R}^{\left( \frac{n-1}{2} \right)}}\]

    C)                 \[{{R}^{n}}\]     

    D)                 \[{{R}^{\left( \frac{n-2}{2} \right)}}\]

    Correct Answer: A

    Solution :

        \[m{{\omega }^{2}}R\propto \frac{1}{{{R}^{n}}}\]Þ \[m\left( \frac{4{{\pi }^{2}}}{{{T}^{2}}} \right)R\propto \frac{1}{{{R}^{n}}}\]Þ \[{{T}^{2}}\propto {{R}^{n+1}}\] \\[T\propto {{R}^{\left( \frac{n+1}{2} \right)}}\]


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