A) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{2} \right]\]
B) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]
C) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]
D) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{{}} \right]\]
Correct Answer: D
Solution :
We know that \[g=\frac{GM}{R_{e}^{2}}\] \[\Rightarrow \] \[GM=gR_{e}^{2}\] \[\Rightarrow \] \[G\rho :\frac{4}{3}\pi R_{e}^{3}=gR_{e}^{2}\] \[\Rightarrow \] \[\rho =\frac{\left[ \frac{g}{G} \right]}{\frac{4}{3}\pi {{R}_{e}}}\]
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