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(B) The power $P$ radiated from a black body is given by Stefan's Boltzmann Law as $P = \sigma A T^4$ ... $(i)$For a spherical body,the surface area $

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$\frac{1}{4}$ times of initial value

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(B) The power $P$ radiated from a black body is given by Stefan's Boltzmann Law as $P = \sigma A T^4$ ... $(i)$For a spherical body,the surface area $A = 4 \pi R^2$ ... (ii)It is given that the temperature $T$ is inversely proportional to the radius $R$,so $T \propto \frac{1}{R}$ or $T = \frac{k}{R}$ ... (iii)Substituting equations (ii) and (iii) into equation $(i)$:$P = \sigma (4 \pi R^2) \left( \frac{k}{R} \right)^4$$P = \sigma 4 \pi R^2 \cdot \frac{k^4}{R^4}$$P = \frac{4 \pi \sigma k^4}{R^2}$Thus,$P \propto \frac{1}{R^2}$.When the radius is doubled $(R' = 2R)$,the new power $P'$ is:$P' \propto \frac{1}{(2R)^2} = \frac{1}{4R^2} = \frac{1}{4} P$Therefore,the radiating power becomes $\frac{1}{4}$ times the initial value.

The temperature of a spherical black body is inversely proportional to its radius. If its radius is doubled,then the power radiating from it will be

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