Question

Three disc A, B and C having radii 2m, 4m and 6 m respectively are rotated 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-

• A. $Q_A$ is maximum
• B. $Q_B$ is maximum
• C. $Q_C$ is maximum
• D. $Q_A=Q_B=Q_C$

Answer 1

Answer: (B)

$Q_B$ is maximum

according to Wein's displacement law $\lambda T$ = constant

So ratio of temperatures of the three discs will be 1/3:1/4:1/5=20:15:12

and ratio of area of the discs = 1:4:9

now according to Stephan's law $Q\alpha A\ast T^4$

so ratio $Q_a:Q_b:Q_c=1\ast (20{)}^4:4\ast (15{)}^4:9\ast (12{)}^4$

on solving we will get that $Q_b$ is maximum