A) 41.4%
B) 50%
C) 82.8%
D) 100%
Correct Answer: A
Solution :
The velocity with which satellite is orbiting around the earth is the orbital velocity \[({{v}_{0}})\] and that required to escape out of gravitational pull of earth is the escape velocity \[({{v}_{es}})\]. We know that __ \[{{v}_{es}}=\sqrt{2gR}\] and \[{{v}_{0}}=\sqrt{gR}\] \[\therefore \] Increase in velocity required \[=\frac{{{v}_{es}}-{{v}_{0}}}{{{v}_{0}}}=\frac{\sqrt{2gR}-\sqrt{gR}}{\sqrt{gR}}\] \[=\sqrt{2}-1\] = 0.414 Percent increase in velocity required \[=0.414\times 100\] = 41.4%
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