A) \[1/3\]
B) \[{{(1/3)}^{1/3}}\]
C) \[1/\sqrt{3}\]
D) \[\sqrt{3}/1\]
Correct Answer: B
Solution :
Rate of cooling \[(R)=\frac{\Delta \theta }{t}=\frac{A\in \sigma ({{T}^{4}}-T_{0}^{4})}{mc}\] Þ \[R\propto \frac{A}{m}\propto \frac{\text{Area}}{\text{volume}}\propto \frac{{{r}^{2}}}{{{r}^{3}}}\propto \frac{1}{r}\] Þ Rate \[(R)\propto \frac{1}{r}\propto \frac{1}{{{m}^{1/3}}}\]\[\left[ \because \,\ m=\rho \times \frac{4}{3}\pi {{r}^{3}}\Rightarrow r\propto {{m}^{1/3}} \right]\] Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}={{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{1/3}}={{\left( \frac{1}{3} \right)}^{1/3}}\]You need to login to perform this action.
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