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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    A satellite is rotating around a planet in the orbit of radius \[r\] with time period\[T\]. If gravitational force changes according to\[{{r}^{5/2}}\], the \[{{T}^{2}}\] will be

    A) \[\propto {{r}^{3}}\]                                      

    B) \[\propto {{r}^{7/2}}\]

    C) \[{{\propto }^{9/12}}\]                                 

    D)  \[\propto {{r}^{3/2}}\]

    Correct Answer: B

    Solution :

    \[\frac{GMm}{{{r}^{5/2}}}=\frac{m{{v}^{2}}}{r}\]                 \[{{v}^{2}}=\frac{GM}{{{r}^{3/2}}}\]                 \[{{T}^{2}}={{\left( \frac{2\pi r}{v} \right)}^{2}}\]                 \[=\frac{4{{\pi }^{2}}{{t}^{2}}}{GM/{{r}^{3/2}}}=\frac{4{{\pi }^{2}}{{r}^{7/2}}}{Gm}\]                 \[{{T}^{2}}\propto {{r}^{7/2}}\]


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