JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer
    Statement-1: Orbital velocity of a satellite is greater than its escape velocity.
    Statement-2: Orbit of a satellite is within the gravitational field of earth whereas escaping is beyond the gravitational field of earth.

    A)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

    B)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

    C)  Statement-1 is true, Statement-2 is false.

    D)  Statement-1 is false, Statement-2 is true.

    Correct Answer: D

    Solution :

     The orbital velocity, if a satellite close to earth is   \[{{v}_{0}}=\sqrt{g{{R}_{e}}},\] While the escape velocity for a body thrown from the earth's surface is \[{{v}_{e}}=\sqrt{2g{{R}_{e}}}\] Thus,   \[\frac{{{v}_{0}}}{{{v}_{e}}}=\frac{\sqrt{g{{R}_{e}}}}{\sqrt{2g{{R}_{e}}}}=\frac{1}{\sqrt{2}}\]or   \[{{v}_{e}}=\sqrt{2}{{v}_{0}}\]i.e., if the orbital velocity of a satellite revolving close to the earth happens to increase to \[\sqrt{2}\]times, the satellite would escape.

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