A) \[2.8\text{ }km{{s}^{-1}}\]
B) \[15.6km{{s}^{-1}}\]
C) \[22.4\text{ }km{{s}^{-1}}\]
D) \[44.8\text{ }km{{s}^{-1}}\]
Correct Answer: C
Solution :
Escape velocity at earth is given by \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] Given, \[{{M}_{e}}={{M}_{p}},{{R}_{p}}=\frac{{{R}_{e}}}{4}\] \[\therefore \] \[\frac{{{v}_{p}}}{{{v}_{e}}}=\sqrt{\frac{{{M}_{e}}}{{{M}_{e}}}\times \frac{{{R}_{e}}}{{{R}_{e}}/4}}\] \[=\sqrt{4}=2\] \[{{v}_{p}}=2{{v}_{e}}\] \[=2\times 11.2\] \[=22.4\,km{{s}^{-1}}\]
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