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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

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P_star = 10000P_sun; T_sun = 6000k; T_star = 2000k
We have $\large P\propto AT^4\propto \pi r^2T^4$
$\large \frac {P_1}{P_2}=\left ( \frac {r_1}{r_2} \right )^2\left ( \frac {T_1}{T_2} \right )^4$
$\large \frac {10000P_{sun}}{P_{sun}}=\left ( \frac {r_1}{r_2} \right )^2\left ( \frac {2000}{6000} \right )^4;\; r_1:r_2=900:1$

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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