A) \[\frac{U}{8}\]
B) \[\frac{U}{16}\]
C) \[\frac{U}{4}\]
D) \[\frac{U}{2}\]
Correct Answer: B
Solution :
According to Stefan's law of radiation \[U\propto \,{{T}^{4}}\,(\therefore \,\,U\] is the energy) \[\Rightarrow \,\,\frac{{{U}_{1}}}{{{U}_{2}}}\,={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}({{T}_{1}}=T)\] \[\Rightarrow \,\frac{{{U}_{1}}}{{{U}_{2}}}={{\left( \frac{T}{T/2} \right)}^{4}}(\therefore \,\,{{T}_{2}}=\frac{T}{2})\] Or \[\frac{{{U}_{1}}}{{{U}_{2}}}={{\left( \frac{2}{1} \right)}^{4}}\,\,\,or\,\,\frac{{{U}_{1}}}{{{U}_{2}}}\,=\left( \frac{16}{1} \right)\] Or \[{{U}_{2}}=\frac{{{U}_{1}}}{16}\,\Rightarrow \,{{U}_{2}}=\frac{U}{16}\]
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