JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    The orbital velocity of an artificial satellite in a circular orbit just above earth's surface is \[{{v}_{0}}\].For a satellite orbiting in a circular orbit at an altitude of half of earth's radius is

    A)  \[\sqrt{\frac{3}{2}}{{v}_{0}}\]                  

    B)  \[\sqrt{\frac{2}{3}}\,{{v}_{0}}\]

    C)  \[\sqrt{\frac{5}{3}}\,{{v}_{0}}\]                

    D)  None of these

    Correct Answer: B

    Solution :

     Orbital velocity at an altitude eh from the earth surface \[=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R+h}},\] where R is radius of earth. If          \[h=0,\,\,{{v}_{0}}=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R}}=\sqrt{{{g}_{0}}R}\] If \[h=\frac{R}{2},\,\,v=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R+\frac{R}{2}}}=\sqrt{\frac{2{{g}_{0}}R}{3}}=\sqrt{\frac{2}{3}}{{v}_{0}}\]

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