The radiation emitted by a star A is 10,000 times that of the Sun. If the surface temperature of the Sun and the star are 6000 K and 2000 K respectively, the ratio of the radius of star A and the Sun is . . . .. . . .

Options

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

Answer

C

Explanation

From Stefan - Boltzmann.s law, we have,
`W=esigmaAT^(4)=esigma(4piR^(2))T^(4)(becauseA=4piR^(2))`
`:.WpropR^(2)T^(4)`
`:.(W_(1))/(W_(2))=((R_(1))/(R_(2)))^(2)((T_(1))/(T_(2)))^(4)`
`W_(1)=10000W_(2),T_(1)=2000K,T_(2)=6000K`
`(100)^(2)=((R_(1))/(R_(2)))^(2)((2000)/(6000))^(4)`
`:.100=(R_(1))/(R_(2))xx(1/3)^(2)`
`:.(R_(1))/(R_(2))=(900)/(1)`
`:.(R_(1))/(R_(2))=900:1`