A satellite of mass m is launched vertically upwards with an initial speed u from the…
Physics · NEET · NTA Exams — Gravitation
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches heights R(R = radius of the earth), it ejects a rocket of mass \(\frac{m}{10}\) 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):
- \(\frac{m}{20}\left(u-\sqrt{\frac{2 G m}{3 R}}\right)^{2}\)
- \(5 m\left(u^{2}-\frac{119}{200} \frac{C M}{R}\right)\)
- \(\frac{3 m}{8}\left(u+\sqrt{\frac{5 G M}{6 R}}\right)^{2}\)
- \(\frac{m}{20}\left(u^{2}+\frac{113}{200} \frac{\mathrm{EM}}{\mathrm{R}}\right)\)
Answer
(B) 5 m (u^ 2 - 119 200 C M R )
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