question_answer

The period of revolution of planet A around the Sun is 8 times that of B. The distance of A from the Sun is how many times greater than that of B from the Sun? (a) 2                                       (b) 3      (c) 4                       (d) 5

Answer:

As\[{{T}^{2}}\propto {{R}^{3}},\]So \[4\frac{T_{A}^{2}}{T_{B}^{2}}=\frac{r_{A}^{2}}{r_{B}^{3}}\] or \[\frac{{{r}_{A}}}{{{r}_{B}}}={{\left( \frac{{{T}_{A}}}{{{T}_{B}}} \right)}^{2}}={{(8)}^{2/3}}=4\] or \[{{r}_{A}}=4{{r}_{B}};\] So, \[{{r}_{A}}{{r}_{B}}=4{{r}_{B}}{{r}_{B}}=3{{r}_{B}}\]