A) 2.5km/s
B) 5km/s
C) 1.25km/s
D) 0.25km/s
Correct Answer: A
Solution :
Here: Mass of the moon \[{{M}_{m}}=\frac{{{M}_{e}}}{81}\] Radius of moon \[{{R}_{m}}=\frac{{{R}_{e}}}{4}\] Escape velocity on earth\[=11.2\text{ }km/sec\] The relation for escape velocity is given by \[{{\upsilon }_{es}}=\sqrt{\frac{2GM}{R}}\propto \sqrt{\frac{M}{R}}\] hence \[\frac{{{\upsilon }_{es}}(m)}{{{\upsilon }_{es}}(e)}=\sqrt{\frac{{{M}_{m}}}{{{R}_{m}}}\times \frac{{{R}_{e}}}{{{M}_{e}}}}\] \[=\sqrt{\left( \frac{{{M}_{e}}}{81}\times \frac{4}{{{R}_{e}}} \right)\times \frac{{{R}_{e}}}{{{M}_{e}}}}\] \[=\sqrt{\frac{4}{81}}=\frac{2}{9}\] Or \[{{\upsilon }_{es(m)}}=\frac{2}{9}\times {{\upsilon }_{es(e)}}\] \[=\frac{2}{9}\times 11.2=2.5\,km/s\]
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