Two spheres $P$ and $Q$, of same colour having radii $8\;cm$ and $2\;cm$ are maintained at temperatures ${127^o}C$ and ${527^o}C$ respectively. The ratio of energy radiated by $P$ and $Q$ is
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(c) Total energy radiated from a body $Q = A\varepsilon \sigma {T^4}t$
==> $Q \propto A{T^4} \propto {r^2}{T^4}$ (( $A = 4\pi {r^2})$
==> $\frac{{{Q_P}}}{{{Q_Q}}} = {\left( {\frac{{{r_P}}}{{{r_Q}}}} \right)^2}\,{\left( {\frac{{{T_P}}}{{{T_Q}}}} \right)^4} = {\left( {\frac{8}{2}} \right)^2}\,{\left\{ {\frac{{(273 + 127)}}{{(273 + 527)}}} \right\}^4} = 1$
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