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Gravitation question

2020 · 7 Jan · Shift 1 · Q54
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Gravitation question

2020 · 7 Jan · Shift 1 · Q54

JEE MainPhysicsGravitationMCQ+4 / −1
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass m10{m \over {10}}10m​ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
  1. A
    3m8(u+5GM6R)2{{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2}83m​(u+6R5GM​​)2
  2. B
    m20(u2+113100GMR){m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right)20m​(u2+100113​RGM​)
  3. C
    5m(u2−119100GMR)5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right)5m(u2−100119​RGM​)
  4. D
    m20(u−2GM3R)2{m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2}20m​(u−3R2GM​​)2
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