A) 1/3
B) 1/9
C) 1/27
D) 1/4
Correct Answer: B
Solution :
\[{{\omega }_{\text{body}}}=27{{\omega }_{\text{earth}}}\] \[{{T}^{2}}\propto {{r}^{3}}\Rightarrow {{\omega }^{2}}\propto \frac{1}{{{r}^{3}}}\Rightarrow \omega \propto \frac{1}{{{r}^{3/2}}}\]\\[r\propto \frac{1}{{{\omega }^{2/3}}}\] Þ \[\frac{{{r}_{\text{body}}}}{{{r}_{\text{earth}}}}={{\left( \frac{{{\omega }_{\text{earth}}}}{{{\omega }_{\text{body}}}} \right)}^{2/3}}\]\[={{\left( \frac{1}{27} \right)}^{2/3}}=\frac{1}{9}\]
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