A hot metallic sphere of radius $r$ radiates heat. It's rate of cooling is
Medium
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(d) Rate of cooling ${R_C} = \frac{{d\theta }}{{dt}} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$
==> $\frac{{d\theta }}{{dt}} \propto \frac{A}{V} \propto \frac{{{r^2}}}{{{r^3}}}$
==> $\frac{{d\theta }}{{dt}} \propto \frac{1}{r}$
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