Three spheres, P, Q and R, having radii 4 m, 5 m and 6 m… | MHT CET 2026 (12 May, Shift 1)

Q38MHT CET 2026 · 12 MAY · SHIFT 1Difficult

Thermal Radiation: Black Body, Stefan & Wien

Three spheres, P, Q and R, having radii $4$ m, $5$ m and $6$ m respectively, are coated with lamp black on their outer surfaces. The wavelengths corresponding to maximum intensity (radiated) are $400$ nm, $500$ nm and $600$ nm respectively. If the powers radiated by them are $P_P, P_Q$ and $P_R$ respectively, then $P_P : P_Q : P_R$ is

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Answer: (b)

$P = \sigma (4\pi r^2) T^4$ and $T \propto \frac{1}{\lambda_m}$ , so $P \propto \frac{r^2}{\lambda_m^4}$ .
$P_P : P_Q : P_R = \frac{4^2}{4^4} : \frac{5^2}{5^4} : \frac{6^2}{6^4}$
$= \frac{1}{16} : \frac{1}{25} : \frac{1}{36}$
So the answer is (b).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2026 (12 May, Shift 1)

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