$A$ metal tape is calibrated at $25^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the measurement of length is (Coefficient of linear expansion of metal $= 1 \times 10^{-5} {}^{\circ} C^{-1}$) (in $\%$)

$A$ brass rod of length $50\; cm$ and diameter $3.0\; mm$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250\; ^{\circ}C$,if the original lengths are at $40.0\; ^{\circ}C$? Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand. (Coefficient of linear expansion of brass $= 2.0 \times 10^{-5}\; K^{-1}$,steel $= 1.2 \times 10^{-5}\; K^{-1}$)

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?

$A$ meter scale made of steel reads accurately at $25^{\circ} C$. Suppose in an experiment an accuracy of $0.06 \,mm$ in $1 \,m$ is required, the range of temperature in which the experiment can be performed with this meter scale is (Coefficient of linear expansion of steel is $11 \times 10^{-6} /{ }^{\circ} C$)

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

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).