Why does the density of solid substances change with an increase in temperature?

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system,

Two rods of different metals have coefficients of linear expansion $\alpha_1$ and $\alpha_2$ respectively. Their respective lengths are $L_1$ and $L_2$. At all temperatures,$(L_2 - L_1)$ remains the same. The correct relation is:

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

When a copper sphere is heated,in which of the following will the maximum percentage change be observed?

$A$ circular metallic disc of radius $R$ has a small circular cavity of radius $r$ as shown in the figure. On heating the system: