A) \[{{V}_{e}}\]
B) \[\sqrt{2}{{v}_{e}}\]
C) \[2{{v}_{e}}\]
D) \[2\sqrt{2}{{v}_{e}}\]
Correct Answer: C
Solution :
Velocity of projection of body, at which the body goes out or gravitational field of earth or planet and never return, is called escape velocity. \[{{v}_{e}}=\sqrt{\frac{2\,GM}{R}}\] where G is gravitational constant, M is mass of plant and \[{{R}_{e}}\] is radius. When \[M=8\,M,\,R=2R\], then \[v{{}_{e}}=\sqrt{\frac{2G\,(8M)}{(2\,R)}}\] \[v{{}_{e}}=2\sqrt{\frac{2GM}{R}}\] \[v{{}_{e}}=2\,{{v}_{e}}\]. Note: Escape velocity is independent of mass of body.
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