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 (a) ((T₁)/(T₂))⁴ (b) ((T₁)/(T₂))² (c) ((T₂)/(T₁))⁴ (d) ((T₂)/(T₁))²

Answer: (d). Power P = 4π R² σ T⁴; equal power gives R₁² T₁⁴ = R₂² T₂⁴. (R₁)/(R₂) = ((T₂)/(T₁))² So the answer is (d).

Two spherical black bodies have radii ' R₁ ' and ' R₂ '. Their… | MHT CET 2025 (23 Apr, Shift 1)

Q51MHT CET 2025 · 23 APR · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

Two spherical black bodies have radii ' $R_1$ ' and ' $R_2$ '. Their surface temperatures are $T_1 K$ and $T_2 K$ respectively. If they radiate the same power, the ratio $\frac{R_1}{R_2}$ is

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Answer: (d)

Power $P = 4\pi R^2 \sigma T^4$ ; equal power gives $R_1^2 T_1^4 = R_2^2 T_2^4$ .
$\dfrac{R_1}{R_2} = \left(\dfrac{T_2}{T_1}\right)^2$
So the answer is (d).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2025 (23 Apr, Shift 1)

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