Two spherical bodies of radii $r_1$ and $r_2$ have surface temperatures $T_1$ and $T_2$ respectively. They radiate the same power. The ratio $r_1/r_2$ is . . . . . .

In the $MKS$ system,Stefan's constant is denoted by $\sigma$. In the $CGS$ system,the multiplying factor of $\sigma$ will be:

$A$ human body has a surface area of approximately $1 \,m^2$. The normal body temperature is $10 \,K$ above the surrounding room temperature $T_0$. Take the room temperature to be $T_0=300 \,K$. For $T_0=300 \,K$, and the value of $\sigma T_0^4=460 \,W/m^2$ (where $\sigma$ is the Stefan-Boltzmann constant). Which of the following option(s) is/are correct?
[$A$] The amount of energy radiated by the body in $1 \,s$ is close to $60 \,J$.
[$B$] If the surrounding temperature reduces by a small amount $\Delta T_0 < < T_0$, then to maintain the same body temperature the same (living) human being needs to radiate $\Delta W = 4 \sigma T_0^3 \Delta T_0$ more energy per unit time.
[$C$] Reducing the exposed surface area of the body (e.g., by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation.
[$D$] If the body temperature rises significantly, then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths.

$A$ black rectangular surface of area '$A$' emits energy '$E$' per second at $27^{\circ}C$. If length and breadth are reduced to $(1/3)^{rd}$ of their initial values and temperature is raised to $327^{\circ}C$,then the energy emitted per second becomes:

If the temperature of a perfectly black body is increased by $10\%$,the intensity of radiation emitted by its surface will increase by ......$\%$.

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the sun (where the radius of the Earth is $r_0$).