A) \[1/3{{\upsilon }_{es}}\]
B) \[9{{\upsilon }_{e}}\]
C) \[3{{\upsilon }_{e}}\]
D) \[{{\upsilon }_{e}}\]
Correct Answer: D
Solution :
Here: Escape velocity on surface of the earth\[={{v}_{es}}\] Mass of the earth\[={{M}_{e}}\] Mass of the surface of the planet\[=3{{M}_{e}}\] Radius of planet\[=3{{R}_{e}}\](where\[{{R}_{e}}\]is the radius of earth) As the escape velocity on surface of the earths is \[{{v}_{es}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}}\] Hence, \[\frac{{{v}_{es(e)}}}{{{r}_{es(p)}}}=\sqrt{\frac{{{v}_{e}}}{{{R}_{e}}}\times \frac{{{R}_{p}}}{{{M}_{p}}}}\]
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