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JEE Main & Advanced JEE Main Paper (Held On 11-Jan-2019 Morning)

  • question_answer
    A satellite is revolving in a circular orbit at a height h from the earth surface, such that \[h<<R\] where R is the radius of the earth. Assuming that the effect of earths atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is [JEE Main Online Paper (Held On 11-Jan-2019 Morning]

    A) \[\sqrt{2gR}\]                            

    B) \[\sqrt{gR}(\sqrt{2}-1)\]

    C) \[\sqrt{\frac{gR}{2}}\]               

    D)                  \[\sqrt{gR}\]

    Correct Answer: B

    Solution :

    The escape speed \[({{v}_{e}})\]of the satellite is \[\sqrt{2g(R+h)}\simeq \sqrt{2gR}\]          \[(h<<R)\] The orbital speed \[({{v}_{0}})\]of the satellite at height h is \[\sqrt{g(R+h)}\simeq \sqrt{gR}\] Hence, the minimum increase in speed so that the satellite could escape is                              \[\sqrt{2gR}-\sqrt{gR}=\sqrt{gR}(\sqrt{2}-1)\]


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