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A spherical solid black body of radius 'r' radiates power 'H' and its rate of cooling is 'C'. If density is constant then which of the following is/are true.

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$H \propto r$ and $c \propto r^{2}$

$H \propto r^{2}$ and $c \propto \frac{1}{r}$

$H \propto r$ and $c \propto \frac{1}{r^{2}}$

$H \propto r^{2}$ and $c \propto r^{2}$

answer is B.

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Detailed Solution

$H = σ e A T^{4} \Rightarrow H \propto A \propto r^{2} C = \frac{σ e A}{m s} (4 T s^{3} Δ T) \Rightarrow C \propto \frac{A}{m} \propto \frac{r^{2}}{r^{3}} \propto \frac{1}{r}$

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