A) \[\sqrt{g{{R}_{e}}/2}\]
B) \[\sqrt{g{{R}_{e}}}\]
C) \[(2-\sqrt{2})\sqrt{g{{R}_{e}}}\]
D) \[\sqrt{2g{{R}_{e}}}\]
Correct Answer: C
Solution :
The escape velocity of rocket required to come out from earth is given by \[{{\upsilon }_{e{{s}_{1}}}}=\sqrt{2g{{R}_{e}}}\] The accelerated velocity near earth surface \[{{\upsilon }_{e{{s}_{2}}}}=2\sqrt{g{{R}_{e}}}\] \[\therefore \]At far distance, final velocity of rocket \[{{\upsilon }_{es}}={{\upsilon }_{e{{s}_{2}}}}-{{\upsilon }_{e{{s}_{1}}}}\] \[=2\sqrt{g{{R}_{e}}}-\sqrt{2g{{R}_{e}}}\] \[=\sqrt{g{{R}_{e}}}-(2-\sqrt{2})\] \[=(2-\sqrt{2})\sqrt{g{{R}_{e}}}\]
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