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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/ $m^{3}$ . 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?

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$2 \sqrt{2} m / s$

2 m/s

$4 \sqrt{2} m / s$

$8 \sqrt{2}$ m/s

answer is A.

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Detailed Solution

Orbital speed $v_{0} = \sqrt{\frac{Gm}{R}}$

Hence escape speed $v_{e} = \sqrt{\frac{2 Gm}{R}} = 2 \sqrt{2} m / s$

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