MHT CET202618 April 2026Morning ShiftPhysicsThermal Properties of MatterActual
Two spherical black bodies of radii R₁ and R₂ having surface temperature T₁ and T₂ respectively, radiate the same power. The ratio of R₁ to R₂ will be
Options
- A( T₁ T₂ )^2
- B( T₁ T₂ )^4
- C( T₂ T₁ )^2
- D( T₂ T₁ )^4
Correct answer
C. ( T₂ T₁ )^2
Step-by-step solution
According to the Stefan-Boltzmann law, the power radiated by a spherical black body is given by P = A T^4 = (4 R^2) T^4 . Given that both black bodies radiate the same power, P₁ = P₂ . (4 R₁^2) T₁^4 = (4 R₂^2) T₂^4 R₁^2 T₁^4 = R₂^2 T₂^4 R₁^2 R₂^2 = T₂^4 T₁^4 R₁ R₂ = ( T₂ T₁ )^2 Answer: ( T₂ T₁ )^2