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CMC Medical CMC-Medical Ludhiana Solved Paper-2011

  • question_answer
    The time period of an earth satellite close to the surface of the earth is 83 min. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be

    A)  83 min                                 

    B)  83\[\sqrt{8}\] min

    C)  664 min              

    D)  249 min

    Correct Answer: C

    Solution :

                     Since,   \[\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{r_{1}^{3}}{r_{2}^{3}}\]\[\Rightarrow \]\[\frac{T_{1}^{2}}{T_{2}^{2}}={{\left( \frac{R}{4R} \right)}^{3}}\] (Three earth radii from the surface means four radii from the centre) \[\therefore \]  \[\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{1}{64}\]                 \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{1}{8}\] \[{{T}_{2}}=8\,{{T}_{1}}=8\times 83\] \[{{T}_{2}}=664\,\min \]


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