$A$ black body radiates at the rate of $W$ watts at a temperature $T$. If the temperature of the body is reduced to $T/3$,it will radiate at the rate of (in Watts):

If $A$ represents Boltzmann constant,$B$ represents Planck's constant and $C$ represents speed of light in vacuum,then the quantity having the dimensions of $A^4 B^{-3} C^{-2}$ is

$A$ planet of radius $R_{p}$ is revolving around a star of radius $R^{*}$ which is at temperature $T^{*}$. The distance between the star and the planet is $d$. If the planet's temperature is $f T^{*}$, then $f$ is proportional to

$A$ wire of length $10 \ cm$ and diameter $0.5 \ mm$ is used in a bulb. The temperature of the wire is $1727^{\circ} C$ and power radiated by the wire is $94.2 \ W$. Its emissivity is $\frac{x}{8}$ where $x=$ . . . . . . (Given $\sigma=6.0 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,$\pi=3.14$ and assume that the emissivity of wire material is same at all wavelengths.)

$A$ 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

Radiated energy at $T$ temperature is $E$ for a body of diameter $d$. If the temperature becomes $2T$ and the diameter becomes $d/4$,then the radiated energy will be: