A) \[1 :1\]
B) \[16:1\]
C) \[4:1\]
D) \[1:9\]
Correct Answer: A
Solution :
Energy radiated per second by a body which has surface area A at temperature T given by Stefan?s law is \[E =\sigma A{{T}^{4}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\,{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}={{\left( \frac{1}{4} \right)}^{2}}\,{{\left( \frac{4000}{2000} \right)}^{4}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{16}{16}=\frac{1}{1}=1:1\]
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