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JEE Main 2021 · Physics · Gravitation · medium

A satellite of mass m moves in a circular orbit of radius 2R about the Earth (radius R, surface gravity g). The minimum extra energy that must be…

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A satellite of mass mm moves in a circular orbit of radius 2R2R about the Earth (radius RR, surface gravity gg). The minimum extra energy that must be supplied to shift it to a circular orbit of radius 3R3R is
  1. A. mgR12\dfrac{mgR}{12}
  2. B. mgR6\dfrac{mgR}{6}
  3. C. mgR3\dfrac{mgR}{3}
  4. D. 5mgR12\dfrac{5mgR}{12}
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Answer: (A) mgR12\dfrac{mgR}{12}

Total energy in a circular orbit is E=−GMm2rE=-\dfrac{GMm}{2r} and GM=gR2GM=gR^2. Then ΔE=GMm2(12R−13R)=GMm12R=mgR12\Delta E=\dfrac{GMm}{2}\left(\dfrac1{2R}-\dfrac1{3R}\right)=\dfrac{GMm}{12R}=\dfrac{mgR}{12}. Using only the change in potential energy (mgR6\dfrac{mgR}{6}) ignores the drop in kinetic energy.
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Original question written in the JEE Main 2021 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake