A) 300 : 1
B) 600 : 1
C) 900 : 1
D) 1200 : 1
Correct Answer: C
Solution :
\[Q\propto A{{T}^{4}}\propto {{r}^{2}}{{T}^{4}}\]\[\Rightarrow \frac{{{Q}_{\text{star}}}}{{{Q}_{\text{sun}}}}=\frac{{{r}^{2}}_{\text{star}}.{{T}^{4}}_{\text{star}}}{{{r}^{2}}_{\text{sun}}\times T_{sun}^{4}}\] \[\Rightarrow \frac{10000}{1}=\frac{r_{\text{star}}^{2}}{r_{\text{sun}}^{2}}\times {{\left( \frac{6000}{2000} \right)}^{4}}\]\[\Rightarrow \frac{{{r}_{\text{star}}}}{{{r}_{\text{sun}}}}=\frac{100\times 9}{1}=\frac{900}{1}\]
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