A) 56.0 km/sec
B) 280 km/sec
C) 112 km/sec
D) 56 km/sec
Correct Answer: A
Solution :
\[{{\upsilon }_{escape}}=\sqrt{\frac{2GM}{R}}\propto \sqrt{\frac{M}{R}}\] Hence, \[\frac{{{\upsilon }_{p}}}{{{\upsilon }_{e}}}=\sqrt{\frac{{{M}_{p}}}{{{R}_{p}}}\times \frac{{{R}_{e}}}{{{M}_{e}}}}\] or \[\frac{{{\upsilon }_{p}}}{{{\upsilon }_{e}}}=\sqrt{100\times \frac{1}{4}}=5\] \[{{\upsilon }_{p}}=5\times 11.2=56\,km\text{/}sec\]
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