AIIMS AIIMS Solved Paper-2002

  • question_answer
    If \[I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] be orbital velocity of a satellite in a circular orbital close to the earths surface and \[\cos \phi =-1\] is escape velocity from earth, then relation between the two is:

    A) \[\phi =\pi ,3\pi ,5\pi ,.................\]        

    B)       \[\phi =(2\pi +1)\pi \,n=1,2,3,..............\]                             

    C) \[=\frac{2\pi }{\lambda }\times \]                           

    D) \[\Rightarrow \]

    Correct Answer: C

    Solution :

                    The orbital velocity of a satellite close to earth is given by \[F=-\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}y\]                                      .....(1). where \[\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\], is radius of earth and g is acceleration due to gravity. The escape velocity of a body thrown from earths surface is \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{({{k}_{1}}+{{k}_{2}})m}}\]                                  ???.(2) Thus,       \[\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] \[k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]    \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\]


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