A) 64.5
B) 129
C) 182.5
D) 730
Correct Answer: B
Solution :
According to Kepler's third law, the ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distances from the sun i.e. \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left[ \frac{{{r}_{1}}}{\tfrac{1}{2}{{r}_{1}}} \right]}^{3}}=8\] Þ \[\frac{{{T}_{1}}}{{{T}_{2}}}=2\sqrt{2}\] \[\therefore \] \[{{T}_{2}}=\frac{{{T}_{1}}}{2\sqrt{2}}=\frac{365\,\,\,days}{2\sqrt{2}}=129\,\,days\]
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