The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 K$ and $2000 K$ respectively, the ratio of the radii of the star $A$ and the sun is
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(c) $Q \propto A{T^4} \propto {r^2}{T^4}$$ \Rightarrow \frac{{{Q_{{\rm{star}}}}}}{{{Q_{{\rm{sun}}}}}} = \frac{{{r^2}_{{\rm{star}}}.{T^4}_{{\rm{star}}}}}{{{r^2}_{{\rm{sun}}} \times T_{sun}^4}}$
$ \Rightarrow \frac{{10000}}{1} = \frac{{r_{{\rm{star}}}^2}}{{r_{{\rm{sun}}}^2}} \times {\left( {\frac{{6000}}{{2000}}} \right)^4}$$ \Rightarrow \frac{{{r_{{\rm{star}}}}}}{{{r_{{\rm{sun}}}}}} = \frac{{100 \times 9}}{1} = \frac{{900}}{1}$
$ \Rightarrow \frac{{10000}}{1} = \frac{{r_{{\rm{star}}}^2}}{{r_{{\rm{sun}}}^2}} \times {\left( {\frac{{6000}}{{2000}}} \right)^4}$$ \Rightarrow \frac{{{r_{{\rm{star}}}}}}{{{r_{{\rm{sun}}}}}} = \frac{{100 \times 9}}{1} = \frac{{900}}{1}$
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