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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$Q \propto A T^{4} \propto r^{2} T^{4} \implies \frac{Q_{\text{star}}}{Q_{\text{sun}}} = \frac{r_{\text{star}}^{2} \cdot T_{\text{star}}^{4}}{r_{\text{sun}}^{2} \times T_{\text{sun}}^{4}}$ $\implies \frac{10000}{1} = \frac{r_{\text{star}}^{2}}{r_{\text{sun}}^{2}} \times \left(\frac{6000}{2000}\right)^{4} \implies \frac{r_{\text{star}}}{r_{\text{sun}}} = \frac{100 \times 9}{1} = \frac{900}{1}$
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