A) Independent of \[r\]
B) Proportional to \[r\]
C) Proportional to \[{{r}^{2}}\]
D) Proportional to \[1/r\]
Correct Answer: D
Solution :
Rate of cooling \[{{R}_{C}}=\frac{d\theta }{dt}=\frac{A\varepsilon \sigma ({{T}^{4}}-T_{0}^{4})}{mc}\] Þ \[\frac{d\theta }{dt}\propto \frac{A}{V}\propto \frac{{{r}^{2}}}{{{r}^{3}}}\] Þ \[\frac{d\theta }{dt}\propto \frac{1}{r}\]
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