Two spherical black bodies of radii ${r_1}$ and ${r_2}$ and with surface temperature ${T_1}$and ${T_2}$ respectively radiate the same power. Then the ratio of ${r_1}$ and ${r_2}$ will be
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(a)For black body, $P = A\varepsilon \sigma {T^4}$. For same power $A \propto \frac{1}{{{T^4}}}$
==> ${\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^4}$
==> $\frac{{{r_1}}}{{{r_2}}} = {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^2}$
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