A) 1 : 1
B) 4 : 1
C) 1 : 4
D) 2 : 1
Correct Answer: A
Solution :
According to Stefan's law\[P=A\,\varepsilon \,\sigma \,{{T}^{4}}\] \[\therefore \] \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{A}_{1}}}{{{A}_{2}}}.\frac{T_{1}^{4}}{T_{2}^{4}}\] \[={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}.{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\] \[[\because \,A=\pi {{R}^{2}}]\] \[={{\left( \frac{4}{1} \right)}^{2}}\times {{\left( \frac{2000}{4000} \right)}^{4}}=\frac{1}{1}\]
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