A) \[\sqrt{\frac{3}{2}}{{v}_{0}}\]
B) \[\sqrt{\frac{2}{3}}\,{{v}_{0}}\]
C) \[\sqrt{\frac{5}{3}}\,{{v}_{0}}\]
D) None of these
Correct Answer: B
Solution :
Orbital velocity at an altitude eh from the earth surface \[=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R+h}},\] where R is radius of earth. If \[h=0,\,\,{{v}_{0}}=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R}}=\sqrt{{{g}_{0}}R}\] If \[h=\frac{R}{2},\,\,v=\sqrt{\frac{{{g}_{0}}{{R}^{2}}}{R+\frac{R}{2}}}=\sqrt{\frac{2{{g}_{0}}R}{3}}=\sqrt{\frac{2}{3}}{{v}_{0}}\]
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