The maximum wavelength of black body emission ${\lambda }_{m^{\text{'}}}$ changes with absolute temperature $T$ of body as

Two cylinders of same diameter and length one of iron and other of silver are placed in close contact as shown. If thermal conductivity of silver is $11$ times than that of iron, then temperature of interface A is approximately

Two uniform rods $AB$ and $BC$ have Young's modulus $1.2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $1.5\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ respectively. If coefficient of linear expansion of $AB$ is $1.5\times {10}^{-5} {}^{\circ }\mathrm{C}^{-1}$ and both have equal area of cross section, then coefficient of linear expansion of $BC,$ for which there is no shift of the junction at all temperatures, is

The coefficient of linear expansion of a crystalline substance in one direction is $2\times {10}^{-4} {}^{\circ }\mathrm{C}^{-1}$ and in every direction perpendicular to it is $3\times {10}^{-4} {}^{\circ }\mathrm{C}^{-1}.$ The coefficient of cubical expansion of crystal is equal to