A) \[\frac{3}{2}{{\upsilon }_{0}}\]
B) \[\frac{2}{3}{{\upsilon }_{0}}\]
C) \[\frac{\sqrt{2}}{3}{{\upsilon }_{0}}\]
D) \[\frac{\sqrt{3}}{2}{{\upsilon }_{0}}\]
Correct Answer: C
Solution :
Given: \[{{R}_{1}}={{R}_{e}}\] \[{{R}_{2}}={{R}_{e}}+\frac{{{R}_{e}}}{2}=\frac{3}{2}{{R}_{e}}\] The orbital velocity of satellite is \[{{\upsilon }_{0}}=\sqrt{\frac{G{{M}_{e}}}{R}}\] \[\Rightarrow \] \[{{\upsilon }_{0}}\propto \sqrt{\frac{1}{R}}\] Hence, \[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}=\sqrt{\frac{{{R}_{2}}}{{{R}_{1}}}}\] \[=\sqrt{\frac{3{{R}_{e}}}{2{{R}_{e}}}}=\sqrt{\frac{3}{2}}\] \[{{\upsilon }_{2}}=\sqrt{\frac{2}{3}}{{\upsilon }_{1}}\] \[=\sqrt{\frac{2}{3}}{{\upsilon }_{0}}\] \[(\because {{\upsilon }_{1}}={{\upsilon }_{0}})\]
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