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

For spherical black body of radius r and absolute temperature T, Power radiated `= sigma (4pi r^(2))T^(4)`
As the same power is radiated in both the cases.
`:. r_(1)^(2) T_(1)^(4) = r_(2)^(2) T_(2)^(4) or ((r_(1))/(r_(2)))^(2) = ((T_(2))/(T_(1)))^(4) or (r_(1))/(r_(2)) = ((T_(2))/(T_(1)))^(2)`