A) \[5\,\,km/s\]
B) \[2.5\,\,km/s\]
C) \[0.5\,\,km/\sec \]
D) \[0.14\,\,km/\sec \]
Correct Answer: B
Solution :
Here: Mass of moon\[{{M}_{m}}=\frac{{{M}_{e}}}{81}\] Radius of moon\[{{R}_{m}}=\frac{{{R}_{e}}}{4}\] Escape velocity on the surface of earth \[{{V}_{es(s)}}=11.2\,\,km/s\] The relation for escape velocity is \[v=\sqrt{\frac{2\,\,GM}{R}}\propto \sqrt{\frac{M}{R}}\] Hence \[\frac{{{v}_{es(m)}}}{{{v}_{es(s)}}}=\sqrt{\frac{{{M}_{m}}}{{{R}_{m}}}\times \frac{{{R}_{e}}}{{{M}_{e}}}}\] \[=\sqrt{\frac{{{M}_{e}}}{81}\times \frac{4}{{{R}_{e}}}\times \frac{{{R}_{e}}}{{{M}_{e}}}}=\frac{2}{9}\] \[{{v}_{es(m)}}=\frac{2}{9}\times 11.2=2.5\,\,km/s\]
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