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

The coefficient of linear expansion depends on

Two rods are joined between fixed supports as shown in the figure. The condition for no change in the total length of the system with an increase in temperature is given by:
($\alpha_1, \alpha_2$ = linear expansion coefficients,$A_1, A_2$ = cross-sectional areas of rods,$Y_1, Y_2$ = Young's moduli)

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^{\circ}C$,the coefficient of linear expansion (in per $^{\circ}C^{-1}$) of the metal is :-

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 $mm$)

$A$ 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: