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\[T={{\left( \frac{Q}{4\pi {{R}^{2}}\sigma } \right)}^{1/4}}\]
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