The radiation emitted by a star A is 10000 ti | vedclass

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(C) The energy radiated per unit time by a black body is given by the Stefan-Boltzmann law: $E = \sigma A T^4$, where $\sigma$ is the Stefan-Boltzmann

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$900$

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(C) The energy radiated per unit time by a black body is given by the Stefan-Boltzmann law: $E = \sigma A T^4$, where $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area $(4\pi R^2)$, and $T$ is the absolute temperature.For the sun: $E_{	ext{sun}} = \sigma (4\pi R_{	ext{sun}}^2) T_{	ext{sun}}^4$.For the star $A$: $E_{	ext{star}} = \sigma (4\pi R_{	ext{star}}^2) T_{	ext{star}}^4$.Given that $E_{	ext{star}} = 10000 E_{	ext{sun}}$, we have:$\sigma (4\pi R_{	ext{star}}^2) T_{	ext{star}}^4 = 10000 	imes \sigma (4\pi R_{	ext{sun}}^2) T_{	ext{sun}}^4$.Canceling common terms:$R_{	ext{star}}^2 T_{	ext{star}}^4 = 10000 R_{	ext{sun}}^2 T_{	ext{sun}}^4$.Rearranging to find the ratio of radii:$\left(\frac{R_{	ext{star}}}{R_{	ext{sun}}}ight)^2 = 10000 \left(\frac{T_{	ext{sun}}}{T_{	ext{star}}}ight)^4$.Substituting the given values ($T_{	ext{sun}} = 6000 \ K$, $T_{	ext{star}} = 2000 \ K$):$\left(\frac{R_{	ext{star}}}{R_{	ext{sun}}}ight)^2 = 10000 \left(\frac{6000}{2000}ight)^4 = 10000 	imes (3)^4 = 10000 	imes 81 = 810000$.Taking the square root of both sides:$\frac{R_{	ext{star}}}{R_{	ext{sun}}} = \sqrt{810000} = 900$.Thus, the ratio $R_{	ext{star}} : R_{	ext{sun}} = 900 : 1$.

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively, the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

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