The time period of a pendulum is given by $T=2\pi \sqrt{\frac{I}{g}}$ If the temperature rises by $\mathrm{\Delta }\theta$ and coefficient of linear expansion of the wire is $\alpha$, the change in time period is

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 $r_0$)