A star behaves like a perfectly black body emitting radiant energy The ratio of radiant energy per second by this star to that emitted by another star having 8 times the radius of former, but having temperature, one-fourth that of the former in Kelvin is .

Options

A. `4 : 1`
B. `1 : 4`
C. `1 : 8`
D. `8 : 1`

Answer

A

Explanation

`((dQ)/dt)_(1)/(((dQ)/(dt))_(2))=(sigmaA_(1)T_(1)^(4))/(sigmaA_(2)T_(2)^(4))=(4piR_(1)^(2)T_(1)^(4))/(4piR_(2)^(2)T_(2)^(4))`
` =(1/8)^(2)xx(4/1)^(4)`
`" "[thereforeR_(1)/R_(2)=8andT_(1)/T_(2)=4]`
`=1/64xx256=4`