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(D) The rate of cooling is defined as the rate of change of temperature,given by $\frac{d	heta}{dt} = \frac{P}{mc}$,where $P$ is the power radiated,$

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Proportional to $1/r$

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(D) The rate of cooling is defined as the rate of change of temperature,given by $\frac{d	heta}{dt} = \frac{P}{mc}$,where $P$ is the power radiated,$m$ is the mass,and $c$ is the specific heat capacity.According to the Stefan-Boltzmann law,the power radiated is $P = A\varepsilon\sigma(T^4 - T_0^4)$,where $A$ is the surface area.For a sphere,$A = 4\pi r^2$ and mass $m = ho V = ho (\frac{4}{3}\pi r^3)$.Substituting these into the expression for the rate of cooling:$\frac{d	heta}{dt} = \frac{A\varepsilon\sigma(T^4 - T_0^4)}{mc} = \frac{4\pi r^2 \varepsilon\sigma(T^4 - T_0^4)}{ho (\frac{4}{3}\pi r^3) c}$.Simplifying the expression,we get $\frac{d	heta}{dt} \propto \frac{r^2}{r^3} \propto \frac{1}{r}$.Therefore,the rate of cooling is proportional to $1/r$.

$A$ hot metallic sphere of radius $r$ radiates heat. Its rate of cooling is

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