Two stars A and B radiate maximum energy at wavelength $3.9 \times 10^{-7}$ m and $5.2 \times 10^{-7}$ m respectively. The ratio of the temperature of star A to that of star B will be

A piece of metal of 850 K is dropped into 1 kg of water at 300 K. If equilibrium temperature of water is 350 K then the heat capacity of the metal expressed in $\dfrac{J}{K}$ is $\left(\text{Sp. heat of water} = 1\ \dfrac{\text{cal}}{\text{g}^\circ\text{C}}\right)$

A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at 400 K is $\dfrac{x}{243}$. The value of $x$ is (Temperature of surrounding is 300 K)

A black body is at temperature of 5780 K. The energy of radiation emitted by the body at wavelength 300 nm is $U_1$, at wavelength 500 nm is $U_2$ and that at 900 nm is $U_3$ respectively. Wien's constant $b = 2.89 \times 10^6\ \text{nmK}$. This shows that