Question

A hot metallic sphere of radius $r$ radiates heat. It's rate of cooling is

• A. independent of $r$
• B. proportional to $r$
• C. proportional to $r^2$
• D. proportional to $1/r$

Answer 1

The correct option is D proportional to $1/r$

Rate of cooling, $R_C=\frac{d\theta }{dt}=\frac{\sigma Ae(T^4-T_0^4)}{mc}$
$\Rightarrow \frac{d\theta }{dt}\propto \frac{A}{V}\propto \frac{r^2}{r^3}\Rightarrow \frac{d\theta }{dt}\propto \frac{1}{r}$