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NEET AIPMT SOLVED PAPER MAINS 2010

  • question_answer
    The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius \[{{R}_{1}}\] to another of radius \[{{R}_{2}}({{R}_{2}}>{{R}_{1}})\] is       

    A) \[GmM\left( \frac{1}{R_{1}^{2}}-\frac{1}{R_{2}^{2}} \right)\]     

    B) \[GmM\left( \frac{1}{R_{1}^{{}}}-\frac{1}{R_{2}^{{}}} \right)\]

    C) \[2GmM\left( \frac{1}{R_{1}^{{}}}-\frac{1}{R_{2}^{{}}} \right)\]

    D) \[\frac{1}{2}GmM\left( \frac{1}{R_{1}^{{}}}-\frac{1}{R_{2}^{{}}} \right)\]

    Correct Answer: D

    Solution :

    The kinetic energy changing the orbit of satellite \[KE=\left( -\frac{GMm}{2{{R}_{2}}} \right)-\left( -\frac{GMm}{2{{R}_{1}}} \right)\] \[KE=\frac{GMm}{2}\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\]


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