A) \[1:2~\]
B) \[1:2~\sqrt{2}\]
C) \[1:4\]
D) \[1:\sqrt{2}\]
Correct Answer: B
Solution :
[b] \[g=\frac{GM}{{{R}^{2}}}\] \[M=\rho V=\frac{4}{3}\pi {{R}^{3}}\rho \] \[g=\frac{G}{{{R}^{2}}}=\frac{4}{3}\pi {{R}^{3}}\rho \] \[g=\frac{4}{3}\pi GR\rho \] \[\frac{{{V}_{e}}}{{{V}_{p}}}=\frac{\sqrt{2\frac{4\pi }{3}GR\rho R}}{\sqrt{2\frac{4}{3}\pi G{{R}_{p}}\rho {{R}_{p}}}}=\sqrt{\frac{{{R}^{2}}\rho }{R_{p}^{2}{{\rho }_{p}}}}\] \[\frac{{{V}_{e}}}{{{V}_{p}}}=\sqrt{\frac{{{R}^{2}}\rho }{{{(2R)}^{2}}2\rho }}=\frac{1}{2\sqrt{2}}\]
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