A) \[{{r}_{1}}{{d}_{1}}:{{r}_{2}}{{d}_{2}}\]
B) \[{{r}_{1}}{{d}_{2}}:{{r}_{2}}{{d}_{1}}\]
C) \[r_{1}^{2}{{d}_{1}}:r_{2}^{2}{{d}_{2}}\]
D) \[{{r}_{1}}:{{r}_{2}}\]
E) \[{{r}_{1}}/\sqrt{{{d}_{1}}}:{{r}_{2}}\sqrt{{{d}_{2}}}\]
Correct Answer: A
Solution :
The relation between density (D) and acceleration due to gravity (g) is \[d=\frac{3g}{4\pi {{R}_{e}}G}\] \[\therefore \] \[\frac{{{d}_{1}}}{{{d}_{2}}}=\frac{{{g}_{1}}}{{{r}_{1}}}\times \frac{{{r}_{2}}}{{{g}_{2}}}\] \[\Rightarrow \] \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{d}_{1}}{{r}_{1}}}{{{d}_{2}}{{r}_{2}}}\]
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