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JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Afternoon)

  • question_answer
    A test particle is moving in a circular orbit in the gravitational field produced by a mass density \[\rho (r)=\frac{K}{{{r}^{2}}}.\]Identify the correct relation between the radius R of the particle's orbit and its period T : [JEE Main 9-4-2019 Afternoon]

    A) \[T/{{R}^{2}}\] is a constant

    B) \[TR\] is a constant

    C) \[{{T}^{2}}/{{R}^{3}}\] is a constant

    D) \[T/R\] is a constant

    Correct Answer: D

    Solution :

    \[m=\int\limits_{0}^{R}{\rho }4\pi {{r}^{2}}dr\] \[m=4\pi KR\] \[\text{v}\propto \sqrt{4\pi K}\] \[\frac{T}{R}=\frac{2\pi }{\sqrt{4\pi K}}.\]


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