Two spherical black bodies have radii ' R₁ ' and ' R₂ '. Their surface temperatures are ' T₁ ' and ' T₂ '. If they radiate same power, then (R₂)/(R₁) is (a) (T₂)/(T₁) (b) (T₁)/(T₂) (c) ((T₂)/(T₁))² (d) ((T₁)/(T₂))²

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

Two spherical black bodies have radii ' R₁ ' and ' R₂ '. Their… | MHT CET 2025 (26 Apr, Shift 2)

Q49MHT CET 2025 · 26 APR · SHIFT 2Medium

Thermal Radiation: Black Body, Stefan & Wien

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

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Answer: (d)

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

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2025 (26 Apr, Shift 2)

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