A) 5.8 years
B) 11.86 years
C) 15.8 years
D) None of these
Correct Answer: B
Solution :
Let \[{{r}_{e}}\,\,and\,{{r}_{P}}\] be distance of earth and planet P from the sun and \[{{\operatorname{T}}_{e}}\,\,and\,\,{{T}_{p}}\] be time period of revolution of earth and planet P around the sun. Now, \[\frac{T_{P}^{2}}{T_{e}^{2}}=\frac{r_{P}^{2}}{r_{e}^{2}}\,\,\,\Rightarrow \,\,\,\,\,\,\,\,{{T}_{P}}={{T}_{e}}{{\left( \frac{{{r}_{e}}}{{{r}_{e}}} \right)}^{3/2}}\] \[=\,\,1{{\left( \frac{5.2\,re}{{{r}_{e}}} \right)}^{3/2}}[{{T}_{e}}=1\,year,\,\,\,{{r}_{P}}=5.2\,{{r}_{e}}]\] \[=\,\,\,11.86 year\]
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