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BHU PMT BHU PMT (Mains) Solved Paper-2010

  • question_answer
    At what height from the surface of the earth, the total energy of the satellite is equal to its potential energy at a height of 2R from the surface of earth? (R =radius of earth)

    A)  \[\frac{R}{4}\]                                 

    B)  \[\frac{R}{2}\]

    C)  \[2R\]                                  

    D)  \[4R\]

    Correct Answer: B

    Solution :

                     The total energy of a satellite at a height h \[=-\frac{GMm}{2(R+h)}\] Potential energy at a height 2R from surface of earth                 \[=-\frac{GMm}{(2R+R)}=-\frac{GMm}{3R}\] According to the question, \[-\frac{GMm}{2(R+h)}=-\frac{GMm}{3R}\]                 \[h=\frac{R}{2}\]


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