A) \[2790\,km\text{-}{{s}^{-1}}\]
B) \[27.9\,km\text{-}{{s}^{-1}}\]
C) \[\frac{27.9}{\sqrt{5}}\,km\text{-}{{s}^{-1}}\]
D) \[27.9\sqrt{5}\,km\text{-}{{s}^{-1}}\]
E) \[\frac{2.79}{\sqrt{5}}km\text{-}{{s}^{-1}}\]
Correct Answer: C
Solution :
Escape velocity, \[{{v}_{e}}=\sqrt{2gR}\] Given, \[g={{(3.1)}^{2}}m{{s}^{-2}}\] \[R=8100\,km=8100\times {{10}^{3}}m.\] \[\therefore \] \[{{v}_{e}}=\sqrt{2\times {{(3.1)}^{2}}\times 8100\times {{10}^{3}}}\] \[{{v}_{e}}=12.5\times {{10}^{3}}m\text{/}s\] \[\Rightarrow \] \[{{v}_{e}}=12.5\,km\text{/}s=\frac{27.9}{\sqrt{5}}km{{s}^{-1}}\]
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