A) \[\frac{{{\operatorname{V}}_{e}}}{\sqrt{2}}\]
B) \[\sqrt{2}{{\operatorname{V}}_{e}}\]
C) \[2{{\operatorname{V}}_{e}}\]
D) \[\frac{{{\operatorname{V}}_{e}}}{2}\]
Correct Answer: B
Solution :
\[\operatorname{Escape} velocity=\sqrt{\frac{GM}{R}}\] \[{{\operatorname{V}}_{e}}=\sqrt{\frac{GM}{R}}\] ?.(1) \[u=\sqrt{\frac{G{{M}_{P}}}{{{R}_{P}}}}\] \[{{\operatorname{M}}_{P}}=\frac{M}{2},\,\,{{R}_{P}}=\frac{R}{4}\] \[u=\sqrt{\frac{GM}{2\times R}\times 4}\] \[\operatorname{u}=\sqrt{\frac{2GM}{R}}\] ?.(2) By (1) and (2) \[\operatorname{u}=\sqrt{2}\,\,{{V}_{e}}\]
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