A) \[{{\upsilon }_{es\,}}\]
B) \[2{{\upsilon }_{es\,(\upsilon )}}\]
C) \[4{{\upsilon }_{es\,}}\]
D) \[16{{\upsilon }_{es\,(\upsilon )}}\]
Correct Answer: A
Solution :
Escape velocity from the earth is given by \[{{\upsilon }_{es}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] and \[{{\upsilon }_{es(m)}}=\sqrt{\frac{2G{{M}_{p}}}{{{R}_{p}}}}\] hence, \[\frac{{{\upsilon }_{es}}}{{{\upsilon }_{es(p)}}}=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}\times \frac{{{R}_{p}}}{{{M}_{p}}}}\] \[=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}\times \frac{2{{R}_{e}}}{2{{M}_{p}}}}=1\] Hence, \[{{\upsilon }_{es(p)}}={{\upsilon }_{es}}\]
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