A) \[\sqrt{\frac{2}{3}}{{v}_{e}}\]
B) \[\sqrt{\frac{3}{2}}{{v}_{e}}\]
C) \[\frac{\sqrt{2}}{3}{{v}_{e}}\]
D) \[\frac{2}{\sqrt{3}}{{v}_{e}}\]
E) None of these
Correct Answer: A
Solution :
Escape velocity \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] and \[{{v}_{p}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{p}}}}\] \[\therefore \] \[\frac{{{v}_{p}}}{{{v}_{e}}}=\sqrt{\frac{{{M}_{p}}\times {{R}_{e}}}{{{M}_{e}}\times {{R}_{p}}}}\] \[=\sqrt{2\times \frac{1}{3}}=\sqrt{\frac{2}{3}}\] \[{{v}_{p}}=\sqrt{\frac{2}{3}}{{v}_{e}}\]
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