The ratio among the linear expansion coefficient $(\alpha)$,areal expansion coefficient $(\beta)$,and volume expansion coefficient $(\gamma)$ is:

Two metal rods $A$ and $B$ each of length $50 \ cm$ and diameter $4.0 \ mm$ are joined together at temperature $30^{\circ} C$. What is the change in length of the combined rod at $230^{\circ} C$ (in $mm$)? [Given linear expansion coefficients of rods $A$ and $B$ are respectively,$2.0 \times 10^{-5} /^{\circ} C$ and $1.0 \times 10^{-5} /^{\circ} C$]

The difference in length between an iron rod and a copper rod is $10 \ cm$ at all temperatures. If ${\alpha _{Fe}} = 11 \times {10^{ - 6}} \, ^\circ C^{ - 1}$ and ${\alpha _{Cu}} = 17 \times {10^{ - 6}} \, ^\circ C^{ - 1}$,what are their lengths respectively?

Thermal expansion of a solid is due to the

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$,its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

$A$ thin copper wire of length $L$ increases in length by $1\%$ when heated from temperature $T_1$ to $T_2$. What is the percentage change in area when a thin copper plate having dimensions $2L \times L$ is heated from $T_1$ to $T_2$?