On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

Write the relation between the coefficient of linear expansion $(\alpha_l)$,coefficient of area expansion $(\alpha_A)$,and coefficient of volume expansion $(\alpha_V)$.

$A$ thin rod having length $L_0$ at $0\,^{\circ}C$ and coefficient of linear expansion $\alpha$ has its two ends maintained at temperatures $\theta_1$ and $\theta_2$,respectively. Find its new length.

$A$ metal rod $2 \,m$ long increases in length by $1.6 \,mm$, when heated from $0^{\circ} C$ to $60^{\circ} C$. The coefficient of linear expansion of the metal rod is:

$A$ rail track made of steel having length $10\,m$ is clamped on a railway line at its two ends as shown in the figure. On a summer day,due to a rise in temperature by $20\,^oC$,it is deformed as shown in the figure. Find $x$ (displacement of the centre) if $\alpha_{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$.

$A$ hole is drilled in a copper sheet. The diameter of the hole is $4.24 \,cm$ at $27.0^{\circ} C$. What is the diameter of the hole when it is heated to $35^{\circ} C$?