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

  • question_answer
    The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is [MNR 1994]

    A)             \[\frac{3}{2}v\]          

    B)             \[\sqrt{\frac{3}{2}}\,v\]

    C)             \[\sqrt{\frac{2}{3}}\,v\]         

    D)             \[\frac{2}{3}\,v\]

    Correct Answer: C

    Solution :

                    \[v=\sqrt{\frac{GM}{R+h}}\] For first satellite \[h=0\], \[{{v}_{1}}=\sqrt{\frac{GM}{R}}\] For second satellite \[h=\frac{R}{2}\], \[{{v}_{2}}=\sqrt{\frac{2GM}{3R}}\]             \[{{v}_{2}}=\sqrt{\frac{2}{3}}{{v}_{1}}=\sqrt{\frac{2}{3}}v\]


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