A) 1 : 3
B) 3 : 1
C) \[\sqrt{27}:1\]
D) \[1:\sqrt{27}\]
Correct Answer: B
Solution :
We know that \[m=\frac{4}{3}\pi {{r}^{3}}d\] \[\therefore \] \[m\propto {{r}^{3}}\] \[r\propto {{(m)}^{1/3}}\] Here \[\frac{{{r}_{A}}}{{{r}_{B}}}={{\left( \frac{{{m}_{A}}}{{{m}_{B}}} \right)}^{1/3}}\] \[\frac{{{r}_{A}}}{{{r}_{B}}}={{\left( \frac{135}{5} \right)}^{1/3}}\] \[\frac{{{r}_{A}}}{{{r}_{B}}}={{\left( 27 \right)}^{1/3}}\] \[\frac{{{r}_{A}}}{{{r}_{B}}}=\frac{3}{1}\]
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