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  4. Three discs, A, B and C having radii 2 m, 4 m and 6 m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm, respectively. The power radiated by them are QA . QB and QC respectively

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Q. Three discs, A, B and C having radii 2 m, 4 m and 6 m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm, respectively. The power radiated by them are $Q_A . Q_B \, and \, Q_C$ respectively

IIT JEEIIT JEE 2004Thermodynamics

Solution:

$Q \propto AT^4 \, and \, \lambda_m T= constant$ Hence, $ \, \, \, \, \, \, Q \propto \frac{A}{(\lambda_m)^4} \, \, \, or \, \, \, Q \propto \frac{r^2}{(\lambda_m)^4}$ $Q_A : Q_B :Q_C =\frac{(2)^2}{(3)^4} : \frac{(4)^2}{(4)^4} : \frac{(6)^2}{(5)^4}$ $ \, \, \, \, \, \, \, \, \, \, =\frac{4}{81} :\frac{1}{16} : \frac{36}{625} =0.05 : 0.0625 : 0.0576$ i.e. Q$_b$ is maximum. Hence, the correct option is (b)