Two rods of different metals have coefficients of linear expansion $\alpha_1$ and $\alpha_2$ respectively. Their respective lengths are $L_1$ and $L_2$. At all temperatures,$(L_2 - L_1)$ remains the same. The correct relation is:

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?

An equilateral triangle $ABC$ is formed by two copper rods $AB$ and $BC$ and one aluminium rod $AC$. The system is heated such that the temperature of each rod increases by $\Delta T$. Find the change in the angle $\angle ABC$. (Coefficient of linear expansion for copper is $\alpha_1$ and for aluminium is $\alpha_2$).

Solids expand on heating because

$A$ pendulum clock shows the correct time at $20\,^oC$. The coefficient of linear expansion of the pendulum material is $12 \times 10^{-6}\,^oC^{-1}$. How much time in $sec/day$ will it lose at $40\,^oC$?

$A$ circular copper ring at $30^{\circ} C$ has a hole with an area of $9.98 \ cm^2$. It is made to slip onto a steel rod of cross-sectional area of $10 \ cm^2$, by raising the temperature of both the ring and the rod simultaneously by an amount $\Delta T$. If the coefficients of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} C$ and $11 \times 10^{-6} /{ }^{\circ} C$ respectively, then the minimum value of $\Delta T$ should be: (in $^{\circ} C$)