MHT CET Medical202622 April 2026Morning ShiftPhysicsThermal Properties of MatterActual
Two spherical black bodies have radii R₁ and R₂ . Their surface temperatures are T₁ K and T₂ K respectively. If they radiate the same power, the ratio R₁ R₂ is
Options
- A( T₁ T₂ )^4
- B( T₁ T₂ )^2
- C( T₂ T₁ )^4
- D( T₂ T₁ )^2
Correct answer
D. ( T₂ T₁ )^2
Step-by-step solution
According to the Stefan-Boltzmann law, the power radiated by a black body is given by P = A T^4 . For a spherical body of radius R , the surface area is A = 4 R^2 . The radiated power is P = (4 R^2) T^4 . Given that both 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