The radiation emitted by a star A is 100 times that of the sun. If the surface temperatures of the sun and the star are 6000 K and 2000 K respectively, then the ratio of the radii of the star and the sun is

Options

A. `30 : 1`
B. `90 : 1`
C. `60 : 1`
D. `100 : 1`

Answer

B

Explanation

`EpropAT^(4)orEpropR^(2)T^(4)" "(becauseA=4piR^(2))`
`thereforeE_(1)/E_(2)=(R_(1)^(2)T_(1)^(4))/(R_(2)^(2)T_(2)^(4))" "thereforeR_(1)/R_(2)=sqrt(E_(1)/E_(2)xxT_(2)^(4)/T_(1)^(4))`
`=sqrt(100/1xx(3/4)^(4))=90`