If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on the earth to what it was previously will be

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:

If the temperature of the sun is decreased by $1 \%$,then the value of the solar constant will change by ........... $\%$

$A$ solid copper sphere of density $\rho$,specific heat capacity $C$ and radius $r$ is initially at $200 \ K$. It is suspended inside a chamber whose walls are at $0 \ K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \ K$ is ( $\sigma$ is Stefan's constant and all the quantities are in $SI$ units.)

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 $: 1$)

The total radiative power emitted by a spherical black body with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved,then the radiative power will be