Solids expand on heating because ................

Brass and lead rods of length $80 \ cm$ are connected in parallel at $0^{\circ}C$. If they are heated to $100^{\circ}C$,what will be the difference in length between their ends in $mm$? (Given: $\alpha_{brass} = 18 \times 10^{-6} \ ^{\circ}C^{-1}$ and $\alpha_{lead} = 28 \times 10^{-6} \ ^{\circ}C^{-1}$)

When the temperature of a body increases from $T$ to $T+\Delta T$, its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body, then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

What is the change in volume of an iron sphere of volume $500 \,cm^3$, when it is heated from $0^{\circ} C$ to $100^{\circ} C$ (in $\,cm^3$)? (Given: $\alpha_{\text{Iron}} = 12 \times 10^{-6} /^{\circ} C$)

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

Steel rails are laid with gaps to allow for thermal expansion. Each track is $10 \ m$ long,when laid at a temperature of $17^{\circ} C$. The maximum temperature that can be reached is $45^{\circ} C$. The gap to be kept between the two segments of the railway track is $(\alpha_{\text{steel}} = 1.3 \times 10^{-5} /^{\circ} C)$. (in $mm$)