A) \[\text{3}\sqrt{\text{3}}\text{T}\]
B) \[\frac{\sqrt{\text{3}}}{2}\text{T}\]
C) \[\frac{1}{3\sqrt{\text{3}}}\text{T}\]
D) \[\frac{1}{2}\text{T}\]
Correct Answer: A
Solution :
According to Keplers law, \[{{T}^{2}}\propto {{R}^{3}}\] \[\therefore \] \[T\propto {{R}^{3/2}}\] \[\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3/2}}={{\left( \frac{R}{3R} \right)}^{3/2}}=\frac{1}{3\sqrt{3}}\] \[{{T}_{2}}=3\sqrt{3}\,\,{{T}_{1}}=3\sqrt{3}T\]
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