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JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    At what height from the earth's surface, the acceleration due to gravity will be half the value of \[g\] at surface? \[(R=6400\,\,km)\]

    A) \[6400\,\,km\]                 

    B)  \[8200\,\,km\]

    C) \[4800\,\,km\]                 

    D)  \[1600\,\,km\]

    Correct Answer: D

    Solution :

    Acceleration due to gravity at a height \[h\] is given by                 \[g'=g\left( 1-\frac{2h}{R} \right)\]                                           ? (i) At height\[h,\,\,g'=\frac{g}{2}\]                       (given) Thus, Eq. (i) becomes \[\therefore \]  \[\frac{g}{2}=g\left( 1-\frac{2h}{R} \right)\] or            \[\frac{1}{2}=1-\frac{2h}{R}\] or            \[\frac{2h}{R}=1-\frac{1}{2}=\frac{1}{2}\] or            \[h=\frac{R}{4}=\frac{6400}{4}=1600\,\,km\]


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