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DUMET Medical DUMET Medical Solved Paper-2009

  • question_answer
    A synchronous satellite goes around the earth once in every 24 h. What is the radius of orbit of the synchronous satellite in terms of the earths radius?   (Given   mass   of   the   earth, \[{{m}_{e}}=5.98\times {{10}^{24}}\,kg,\] radius of the earth, \[{{r}_{e}}=6.37\times {{10}^{6}}\,m,\]   Universal   constant   of gravitation, \[G=6.67\times {{10}^{-11}}N-{{m}^{2}}k{{g}^{-2}})\]

    A)  \[2.4\,{{r}_{e}}\]            

    B)  \[3.6\,{{r}_{e}}\]

    C)  \[4.8\,{{r}_{e}}\]            

    D)  \[6.6\,{{r}_{e}}\]

    Correct Answer: D

    Solution :

     Time period of satellite \[T=2\pi \sqrt{\frac{{{r}^{3}}}{G{{M}_{e}}}}\] or \[{{T}^{2}}=\frac{4{{\pi }^{2}}{{r}^{3}}}{G{{M}_{e}}}\] ... (i) Also \[g=\frac{G{{M}_{e}}}{r_{e}^{2}}\] ?. (ii) From Eqs. (i) and (ii), we get \[{{T}^{2}}=\frac{4{{\pi }^{2}}{{r}^{3}}}{gr_{e}^{2}}\] ... (iii) Substituting the given values in Eq. (iii), we get \[{{(24\times 60\times 60)}^{2}}=\frac{4\times {{(3.14)}^{2}}{{r}^{3}}}{9.8r_{e}^{2}}\] or \[r=6.6\,{{r}_{e}}\]


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