A) \[{{(Kg)}^{1/2}}\]
B) \[{{(Kg)}^{-1/2}}\]
C) \[{{(Kg)}^{2}}\]
D) \[{{(Kg)}^{-2}}\]
Correct Answer: A
Solution :
At a certain velocity of projection the body will go out of the gravitational field of earth and never return to earth, this initial velocity is known as escape velocity. \[{{v}_{e}}=\sqrt{2gR}\] where g is acceleration due to gravity and R is radius. Given, \[\frac{{{R}_{1}}}{{{R}_{2}}}=K,\frac{{{g}_{1}}}{{{g}_{2}}}=g\] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{\sqrt{{{g}_{1}}{{R}_{1}}}}{\sqrt{{{g}_{2}}{{R}_{2}}}}=\sqrt{Kg}\] \[\frac{{{v}_{1}}}{{{v}_{2}}}={{(Kg)}^{1/2}}\]
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