The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

$A$ black body at a high temperature $T \ K$ radiates energy at the rate $E \ W/m^2$. When the temperature falls to $(T/2) \ K$,the radiated energy will be:

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 ........ $cal$.

Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures $T$ and $2T$, respectively. The temperature of the middle plate in steady state will be close to ........... $T$.

Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively radiate the same power. Then the ratio of $r_1$ and $r_2$ will be:

Energy is being emitted from the surface of a black body at $127\,^{\circ}C$ temperature at the rate of $1.0 \times 10^6\,J/s\cdot m^2$. The temperature of the black body at which the rate of energy emission is $16.0 \times 10^6\,J/s\cdot m^2$ will be ......... $^{\circ}C$.