$A$ pendulum clock shows the correct time at $20^{\circ}C$. During summer days,when the temperature rises to $40^{\circ}C$,what will be the time change in the clock in one day (in $.64$)? (Given: $\alpha = 10^{-5} {^{\circ}C}^{-1}$)

$A$ rod of length $2 \ m$ at $0^\circ C$ has a linear expansion coefficient $\alpha = (3x + 2) \times 10^{-6} \ ^\circ C^{-1}$,where $x$ is the distance (in $cm$) from one end of the rod. Find the length of the rod at $20^\circ C$ in meters.

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

Why does the density of solid substances change with an increase in temperature?

An iron rod has a length of $10 \ cm$ at $20^{\circ}C$. What will be the change in length of the iron rod at $19^{\circ}C$? (Given for iron,$\alpha = 11 \times 10^{-6} \ ^{\circ}C^{-1}$)

$A$ 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 $\alpha_{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$.