If the temperature of the body is increased by $10\%$,the percentage increase in the emitted radiation will be ....... $\%$

$A$ solid cylinder of radius $r_1=2.5 \ cm$, length $l_1=5.0 \ cm$ and temperature $40^{\circ}C$ is suspended in an environment of temperature $60^{\circ}C$. The thermal radiation transfer rate for the cylinder is $1.0 \ W$. If the cylinder is stretched until its radius becomes $r_2=0.50 \ cm$, the thermal radiation transfer rate is changed to (in $W$)

The temperature of a black body is increased by $50 \%$. The percentage increase in the rate of radiation by the body is approximately: (in $\%$)

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

$A$ 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.

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio $1:4$. Then the ratio $T_1: T_2$ is