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Q.

The radiation emitted by a star "A" per second is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000K and 2000K respectively, the ratio of the radii of the star A and the sun is

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a

300 : 1

b

600 : 1

c

900 : 1

d

1200 : 1

answer is C.

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Detailed Solution

P_star = 10000 P_sun; T_sun = 6000k, T_star = 2000k
we have $p \propto {AT}^{4} \propto {πr}^{2} T^{4}$
$\frac{p_{1}}{p_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} {(\frac{T_{1}}{T_{2}})}^{4} \frac{10000 P_{sun}}{P_{sun}} = {(\frac{2000}{6000})}^{4} {(\frac{r_{1}}{r_{2}})}^{2}; r_{1} : r_{2} = 900 : 1$

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