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

Show that the coefficient of area expansion,$(\Delta A / A) / \Delta T,$ of a rectangular sheet of a solid is twice its linear expansivity,$\alpha_{l}$.

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

$A$ circular disc with a hole is shown in the figure. On heating,if the outer diameter $d_1$ increases by $0.3\%$,then the inner diameter $d_2$ will

$A$ steel tape gives correct measurement at $20^{\circ} C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ} C$. The reading is $25 \ cm$ on the tape. The real length of the given piece of wood must be:

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 $mm$)