Q.

The radiation emitted by a star A is 1000 times that of the sun. If the surface temperatures of the sun and star A are 6000 K and 2000 K, 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

According to Stefan-Boltzmann law, the energy radiated per second through the surface of area A is given byE = σAT4 ∴ E1E2=A1A2T1T24 or  10000=r12r22200060004 or   r12r22=(30)4 or   r1:r2=900:1
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The radiation emitted by a star A is 1000 times that of the sun. If the surface temperatures of the sun and star A are 6000 K and 2000 K, respectively, the ratio of the radii of the star A and the sun is