Find the heat current flowing through a hollow thick sphere of inner radius $R$ and outer radius $2 R$. Thermal conductivity of metal is $K$. Temperature inside sphere is $T_1$ and outside sphere is $T_2·\left(T_1-T_2=\frac{10}{\pi KR}\right)$

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