The little prince (the main character of the novel written by Antoine de Saint-Exupery) lives on the spherical planet named B-612, the density of which is 5200 kg/m3. The Little Prince noticed that if he quickens his pace, he feels himself lighter. When he reached the speed of 2 m/s he became weightless, and began to orbit about the planet as a satellite. What is escape speed on the surface of planet?

Question

The little prince (the main character of the novel written by Antoine de Saint-Exupery) lives on the spherical planet named B-612, the density of which is 5200 kg/m3. The Little Prince noticed that if he quickens his pace, he feels himself lighter. When he reached the speed of 2 m/s he became weightless, and began to orbit about the planet as a satellite. What is escape speed on the surface of planet? (A) 2√2 m/s (B) 2 m/s (C) 4√2 m/s (D) 8√2 m/s

Tardigrade Admin · Accepted Answer

Orbital speed v0 =√(Gm/R) 2 = √(Gm/R) Hence escape speed ve = √(2Gm/R) = 2√2 m/s

$22 m / s$

$2 m / s$

$42 m / s$

$82 m / s$

Orbital speed $v_{0} = \frac{G m}{R} 2 = \frac{G m}{R}$

Hence escape speed $v_{e} = \frac{2 G m}{R}$

$= 22 m / s$

22​m/s

2m/s

42​m/s

82​m/s

Orbital speed v0​=RGm​​2=RGm​​ Hence escape speed ve​=R2Gm​​ =22​m/s

$22 m / s$

$2 m / s$

$42 m / s$

$82 m / s$

Orbital speed $v_{0} = \frac{G m}{R} 2 = \frac{G m}{R}$

Hence escape speed $v_{e} = \frac{2 G m}{R}$

$= 22 m / s$