$A$ solid sphere at a temperature $T \ K$ is cut into two hemispheres. The ratio of energies radiated by one hemisphere to the whole sphere per second is

If the temperature of a perfectly black body is reduced from $T$ to $T/2$,find the percentage decrease in the rate of emission.

What is the ratio of energy emitted by a black body at temperatures $27^{\circ}C$ and $927^{\circ}C$?

$A$ black body at $227^{\circ}C$ radiates heat at the rate of $20 \, cal \, m^{-2} \, s^{-1}$. When its temperature is raised to $727^{\circ}C$,the rate of heat radiation will be $x \, cal \, m^{-2} \, s^{-1}$. Find $x$.

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 $: 1$)

Two spherical black bodies have radii $R_1$ and $R_2$. Their surface temperatures are $T_1 \ K$ and $T_2 \ K$ respectively. If they radiate the same power,the ratio $\frac{R_1}{R_2}$ is