If the temperature of a rod is increased in such a way that no linear expansion occurs,then the stress developed in the rod does not depend on .......

$A$ metal rod of length $20 \, cm$ expands by $0.075 \, cm$ when its temperature is raised from $0 \, ^\circ C$ to $100 \, ^\circ C$. Another rod $B$ of a different metal of the same length expands by $0.045 \, cm$ for the same rise in temperature. $A$ third rod of the same length is composed of two metals $A$ and $B$ joined together. This composite rod expands by $0.060 \, cm$ for the same temperature difference. The length of the portion of metal $A$ is ..... $cm$.

The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of the crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$.

$A$ steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text{steel}} = 1.2 \times 10^{-5} {}^{\circ} C^{-1}\right]$

Two different wires having lengths $L_{1}$ and $L_{2}$ and respective temperature coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is

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