Who Is The Big Brother?

1. Wien's displacement law says that $\lambda_{max} \propto \frac{1}{T}$ . Since the temperature of $A$ is three times the temperature of $B$ , $\lambda_{max}$ of $A$ must be one third that of $B$ .

2. Stefan–Boltzmann law says that the power per unit area is directly proportional to $T^4$ . Since the temperature of $A$ is three times that of $B$ , the power per unit area of $A$ is $3^4 = 81$ times that of $B$ .

3. From the result in 2, the power per unit area of $A$ is $81$ times that of $B$ . In addition, since the radius of $A$ is one third that of $B$ , the area of $A$ is $\frac{1}{9}$ that of $B$ . Thus the power of $A$ is $81 \times \frac{1}{9} = 9$ times that of $B$

1.Well this was quite simple. The first answer can be given from Wein's displacement law. It just comes out to be the ratio of the two temperatures in this case.

2.2nd Answer is from Stephan's Law of Radiation. The energy emitted per unit time and per unit area is proportional to $T^{4}$ where T is temperature of the body. Here the ratio comes out to be
$\frac{9000^{4}}{3000^{4}}$

3.Last result can be obtained from multiplying result two by the corresponding areas and taking the ratio.

So finally it comes out to be a,b,c all three correct.