A) \[Q/4\pi {{R}^{2}}\sigma \]
B) \[{{(Q/4\pi {{R}^{2}}\sigma )}^{-1/2}}\]
C) \[{{(4\pi {{R}^{2}}Q/\sigma )}^{1/4}}\]
D) \[{{(Q/4\pi {{R}^{2}}\sigma )}^{1/4}}\]
Correct Answer: D
Solution :
| From Stefan' law, |
| \[E=\sigma {{T}^{4}}\] |
| So, the rate energy production |
| \[Q=E\times A\] |
| \[Q=\sigma {{T}^{4}}\times 4\pi {{R}^{2}}\] |
| Temperature of star \[T={{\left( \frac{Q}{4\pi {{R}^{2}}\sigma } \right)}^{1/4}}\] |
| (\[\sigma \] stands for Stefan's constant.) |
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