Three rods $AB, BC, CA$ are joined to form a triangle $ABC$. Length of the rods $AB$ and $AC$ each are equal to $b$ and their coefficient of linear expansion is ${\alpha }_1$ whereas length of $\text{rod} BC$ is $a$ and its coefficient of linear expansion is ${\alpha }_2.$ Ratio $\frac{b}{a}$, such that the height $h$ does not change upon heating the rods by same temperature, is $\frac{1}{n}\sqrt{\frac{{\alpha }_2}{{\alpha }_1}}$. Value of $n$, is

The figure shows a composite rod made of two different material of thermal conductivity $\left(\frac{K}{4}\right)$ and $K$ respectively. The length of two rods are shown in figure. If the end temperature are $T_1$ and $T_2$ respectively, then the temperature of interface is $\frac{T_1+n{T}_2}{n+1}·$ Value of $n$, is

A brass rod and an aluminium rod each of length $1 \mathrm{m}$ and same cross section area $1{ \mathrm{cm}}^2$ are placed in contact with each other as shown. Temperature of both the rods is raised by $100 K$. The coeffcients of linear expansion of brass and aluminium are $2.0\times {10}^{-5}{ \mathrm{K}}^{-1}$ and $2.4\times {10}^{-5}{ \mathrm{K}}^{-1}$ respectively. If the Young's moduli of brass and aluminium are ${10}^{11} \mathrm{N} {\mathrm{m}}^2$ and $7\times {10}^{10} \mathrm{N} {\mathrm{m}}^2$ respectively then stress in the rods is