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

(2) `u = e sigma 4 pi r^(2) T^(4)`
`R_(1)^(2) T_(1)^(4) = R_(2)^(2) T_(2)^(4)`
`(R_(1))/(R_(2)) = ((T_(2))/(T_(1)))^(2)`