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

Options

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

Answer

B

Explanation

Power radiated `prop A (T^(4))`
`:. 4pi r_(1)^(2) xx (T_(1))^(4) = 4pi r_(2)^(2) (T_(2))^(4) or (r_(1))/(r_(2)) = ((T_(2))/(T_(1)))^(2)`