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

  • question_answer
    The mean radius of the earth is R, its angular speed on its own axis is \[\omega \] and the acceleration due to gravity at earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be                            [CBSE PMT 1992]

    A)             \[{{R}^{2}}g/\omega \]

    B)               \[{{R}^{2}}{{\omega }^{2}}/g\]

    C)             \[Rg/{{\omega }^{2}}\]       

    D)             \[{{R}^{2}}g/{{\omega }^{2}}\]

    Correct Answer: D

    Solution :

                    Orbital velocity \[{{v}_{0}}=\sqrt{\frac{GM}{r}}=\sqrt{\frac{g{{R}^{2}}}{r}}\] and \[{{v}_{0}}=r\omega \] This gives \[{{r}^{3}}=\frac{{{R}^{2}}g}{{{\omega }^{2}}}\]


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