$A$ clock which keeps correct time at $20\,^{\circ}C$ has a pendulum rod made of brass. How many seconds will it gain or lose per day when the temperature falls to $0\,^{\circ}C$? $(\alpha = 18 \times 10^{-6}/^{\circ}C)$

$A$ blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243\; m$ and $5.231\; m$,respectively at $27^{\circ}C$. To what temperature (in $^{\circ}C$) should the ring be heated so as to fit the rim of the wheel? (Given: coefficient of linear expansion of iron $\alpha = 1.20 \times 10^{-5} K^{-1}$)

Railway tracks are made of steel segments separated by small gaps to allow for linear expansion. $A$ segment of the track is $10 \ m$ long when laid at a temperature of $17^{\circ} C$. The maximum temperature that can be reached is $45^{\circ} C$. The increase in the length of the segment of the railway track is $x \times 10^{-5} \ m$. The value of $x$ is (given $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /{ }^{\circ} C$).

$A$ $1$ litre glass flask contains some mercury. It is found that at different temperatures,the volume of air inside the flask remains the same. What is the volume of mercury in this flask in $cc$ if the coefficient of linear expansion of glass is $9 \times 10^{-6} /^{\circ}C$ and the coefficient of volume expansion of mercury is $1.8 \times 10^{-4} /^{\circ}C$?

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:

$A$ clock which keeps correct time at $20^\circ C$ is subjected to $40^\circ C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /^\circ C$,how much time will it gain or lose per day?