The compressional force required to prevent a metallic rod of cross-sectional area $A$ from expanding, when it is heated to increase its temperature by $t°\mathrm{C}$, is (modulus of elasticity is $E$ and coefficient of linear expansion is $\alpha$)

Two metallic rods of equal length and cross-section but thermal conductivities $K_1$ and $K_2$ are welded as shown

The equivalent thermal conductivity of this resulting rod will be

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \mathrm{K}$, evaluate the total radiant power, incident on the earth, at a distance $r$ from the sun:

(radius of earth is $r_0$)