Two spherical bodies of same materials having radii $0.2 \ m$ and $0.8 \ m$ are placed in the same atmosphere. The temperature of the smaller body is $800 \ K$ and the temperature of the bigger body is $400 \ K$. If the energy radiated from the smaller body is $E$,the energy radiated from the bigger body is (assume the effect of the surrounding to be negligible).

Suppose the Sun is a spherical body of radius $r$ with a surface temperature of $t \, ^\circ C$. It radiates energy like a black body. The power received per unit area at a distance $R$ from the center of the Sun will be: ($\sigma$ is the Stefan-Boltzmann constant)

$A$ certain stellar body has radius $50 \,R_{s}$ and temperature $2 \,T_{s}$ and is at a distance of $2 \times 10^{10} \,AU$ from the earth. Here,$AU$ refers to the earth-sun distance and $R_{s}$ and $T_{s}$ refer to the sun's radius and temperature,respectively. Take both the star and the sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

$A$ rectangular black body of temperature $127^{\circ} C$ has surface area $4 \ cm \times 2 \ cm$ and rate of radiation is $E$. If its temperature is increased by $400^{\circ} C$ and surface area is reduced to half of the initial value,then the rate of radiation is:

$A$ cube of side $1 \ m$ has a temperature of $127^{\circ}C$ and an emissivity of $\frac{1}{5.67}$. If the surrounding temperature is $27^{\circ}C$,the rate of loss of heat by radiation is ...... $kW$.

If the temperature of a hot body is increased by $50 \%$,then the increase in the quantity of emitted heat radiation will be approximately (in $\%$)