A) 1.25 km/s
B) 2.49 km/s
C) 3.7 km/s
D) 5.6 km/s
Correct Answer: C
Solution :
[b] On the earth The escape speed is \[{{V}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] on the moon The escape speed is \[{{V}_{m}}=\sqrt{\frac{2G{{M}_{m}}}{{{R}_{m}}}}\] \[\frac{{{V}_{m}}}{{{V}_{e}}}=\sqrt{\left( \frac{{{M}_{m}}}{{{M}_{e}}} \right)\left( \frac{{{R}_{e}}}{{{R}_{m}}} \right)}\] \[=\sqrt{\left( \frac{1}{81} \right)\left( \frac{4}{1} \right)}=\frac{2}{9}\] \[{{V}_{m}}=\frac{2}{9}{{V}_{e}}=\frac{2}{9}\times 11.2\text{ }km/sec\] \[=2.49\text{ }km\text{ }se{{c}^{-1}}\]
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