A) \[{{v}_{e}}={{v}_{p}}\]
B) \[{{v}_{e}}={{v}_{p}}/2\]
C) \[{{v}_{e}}=2{{v}_{p}}\]
D) \[{{v}_{e}}={{v}_{p}}/4\]
Correct Answer: B
Solution :
\[{{v}_{e}}=\sqrt{\frac{2GM}{R}}=R\sqrt{\frac{8}{3}\pi G\rho }\] If mean density is constant then \[{{v}_{e}}\propto R\] \[\frac{{{v}_{e}}}{{{v}_{p}}}=\frac{{{R}_{e}}}{{{R}_{p}}}=\frac{1}{2}\]Þ\[{{v}_{e}}=\frac{{{v}_{p}}}{\text{2}}\]
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