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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Motion of Satellite

  • question_answer
     If \[g\propto \frac{1}{{{R}^{3}}}\] (instead of \[\frac{1}{{{R}^{2}}}),\] then the relation between time period of a satellite near earth's surface and radius R will be                      [RPMT 2002]

    A)             \[{{T}^{2}}\propto {{R}^{3}}\]

    B)               \[T\propto {{R}^{2}}\]

    C)             \[{{T}^{2}}\propto R\]

    D)               \[T\propto R\]

    Correct Answer: B

    Solution :

                    Gravitational force provides the required centripetal force             \[m{{\omega }^{2}}R=\frac{GMm}{{{R}^{3}}}\]\[\Rightarrow \]\[\frac{4{{\pi }^{2}}}{{{T}^{2}}}=\frac{GM}{{{R}^{4}}}\]\[\Rightarrow \]\[T\propto {{R}^{2}}\]


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