A) \[1/3{{\upsilon }_{e}}\]
B) \[9{{\upsilon }_{e}}\]
C) \[3{{\upsilon }_{e}}\]
D) \[{{\upsilon }_{e}}\]
Correct Answer: D
Solution :
Here: Escape velocity on surface of the earth \[={{\upsilon }_{es}}\] 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 \[{{\upsilon }_{es}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}}\] Hence, \[\frac{{{\upsilon }_{es(e)}}}{{{r}_{es(p)}}}=\sqrt{\frac{{{\upsilon }_{e}}}{{{R}_{e}}}\times \frac{{{R}_{p}}}{{{M}_{p}}}}\] Or \[\frac{{{\upsilon }_{es(e)}}}{{{r}_{es(p)}}}=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}\times \frac{3{{R}_{e}}}{3{{M}_{e}}}}=\frac{1}{1}\] Or \[{{\upsilon }_{es(p)}}={{\upsilon }_{es(e)}}\]
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