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

`E=sigma AT ^(4)`
`(E_(1))/(E_(2))=(A_(1))/(A_(2))((t_(1))/(T_(2)))^(4)=(E_(1))/(E_(2))=(r_(1)^(2))/(r_(2)^(2))((T_(1))/(T_(2)))^(4)`
10000=`((r_(1)))/(r_(2))_^(2)((2000)/(6000))^(4)`
`implies r_(1):r_(2)=900:1`