Answer:
We know \[\frac{{{T}^{2}}}{{{R}^{3}}}=const\] Planet-A Planet-B \[{{R}_{A}}={{10}^{13}}m\] \[{{R}_{B}}={{10}^{12}}m\] \[{{T}_{A}};{{T}_{B}}=?\]
\[\Rightarrow \frac{T_{A}^{2}}{T_{B}^{2}}=\frac{R_{A}^{3}}{R_{B}^{3}}={{\left[ \frac{{{R}_{A}}}{{{R}_{B}}} \right]}^{3}}\] \[\frac{{{T}_{A}}}{{{T}_{B}}}={{\left[ \frac{{{R}_{A}}}{{{R}_{B}}} \right]}^{\frac{3}{2}}}\] \[\frac{{{T}_{A}}}{{{T}_{B}}}={{\left[ \frac{{{10}^{13}}}{{{10}^{12}}} \right]}^{\frac{3}{2}}}\] \[=\frac{10\sqrt{10}}{1}\] \[{{T}_{A}}:{{T}_{B}}=10\sqrt{10}:1\]
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