A) 2.83 km/s
B) 3.28 km/sec
C) 6.68 km/s
D) 8.32 km/sec
Correct Answer: B
Solution :
Orbital velocity of space-ship, \[{{v}_{0}}=\sqrt{\frac{GM}{r}}\] \[(\because \,\,r>>R)\] Since\[,\] \[g=\sqrt{\frac{GM}{{{R}^{2}}}}\], \[\therefore \] \[GM=g{{R}^{2}}\] Now, \[{{v}_{0}}=\sqrt{Rg}=\sqrt{6.4\times {{10}^{6}}\times 9.8}\] \[=7.9195\,\,km/s\] Again, \[{{v}_{e}}=\sqrt{2rg}=\sqrt{2\times 7.9195}\] \[=11.20\,\,km/s\] \[\therefore \]Additional velocity required \[=11.20-7.9195\] \[=\mathbf{3}\mathbf{.28}\,\,\mathbf{km/sec}\]
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