The radiation emitted by a star A is 10,000 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

Options

A. `300:1`
B. `600:1`
C. `900:1`
D. `1200:1`

Answer

C

Explanation

Since, `Q prop AT^4 implies Q prop r^2T^4`
`implies (Q_("star"))/(Q_("sun"))=((r_("star"))/(r_("sun")))^2((2000)/(6000))^4`
`implies (10000)/(1)=((r_("star"))/(r_("sun")))^2 xx ((2000)/(6000))^4 implies (r_("star"))/(r_("sun"))=900`