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 intensitios are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are $Q_{A},\ Q_{B}$and $\mathcal{Q}_{C}$ respectively
A) $Q_{A}\ is\ maximum$
B) $Q_{B}\ is\ maximum$
C) $Q_{c}\ is\ maximum$
D) $Q_{A} = Q_{B} = Q_{C}$
Explanation
(b) Power radiated, $\mathcal{Q \propto}AT^{4}\ and\ \lambda_{m}T = constant.Hence,\mathcal{Q \propto}\frac{A}{\left( \lambda_{m} \right)^{4}}$
$\mathcal{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Q \propto}\frac{A}{\left( \lambda_{m} \right)^{4}}$
or $\mathcal{\ \ \ \ \ \ \ \ \ Q \propto}\frac{r^{2}}{\left( \lambda_{m} \right)^{4}}$
$\mathcal{Q}_{A}:\mathcal{Q}_{B}:\mathcal{Q}_{C} = \frac{(2)^{2}}{(3)^{4}}:\frac{(4)^{2}}{(4)^{4}}:\frac{(6)^{2}}{(5)^{4}}$
$= \frac{4}{81}:\frac{1}{16}:\frac{36}{625}$
= 0.05:0.0625:0.0576
$ie.,\ \mathcal{Q}_{B}$ is maximum.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.