Two spherical black bodies of radii `R_(1)` and `R_(2)` and with surface temperature `T_(1)` and `T_(2)` respectively radiate the same power. `R_(1)//R_(2)` must be equal to

Options

A. `(T_(1)/T_(2))^(2)`
B. `(T_(2)/T_(1))^(2)`
C. `(T_(1)/T_(2))^(4)`
D. `(T_(2)/T_(1))^(4)`

Answer

B

Explanation

According to Stefan's law,
`4pi_(1)^(2)T_(1)^(4) = 4pir_(2)^(2)T_(2)^(4)`
`therefore` `r_(1)/r_(2) = T_(2)^(2)/T_(1)^(2)`