Two spherical black bodies of radii ' r₁ ' and ' r₂ ' at temperature ' T₁ ' and ' T₂ ' respectively radiate power in the ratio 1: 2 Then r₁: r₂ is

Step-by-step solution

Power Radiated by black body, P = AT ^4 For first black body: P ₁= 4 r ₁^2 ~T ₁^4 For second black body: P ₂= 4 r ₂ ^2 ~T ₂ ^4 The ratio will be: aligned & P ₁ P ₂ = 4 r ₁^2 ~T ₁^4 4 r ₂^2 ~T ₂^4 & 1 2 = r ₁^2 ~T ₁^4 r ₂^2 ~T ₂^4 & r ₁^2 r ₂^2 = 1 2 T ₂^4 ~T ₁^4 & r ₁ r ₂ = 1 2 ( T ₂ ~T ₁ )^2 aligned