The distance between Allahabad and Delhi is $600 \mathrm{km}$. Find the total space that must be left between the rails to allow for a change of temperature from $36.5°F$ in winter to $113°F$ in summer. Co-efficient of linear expansion of iron$=0.000012$ per $°C$.

The radius of a wheel is $3 \mathrm{m}$ and that of an iron tyre is $2.992 \mathrm{m}$ at $0° \mathrm{C}$. At what temperature will the tyre fit exactly on the wheel? $\alpha$ for iron$=12\times {10}^{-6}°{\mathrm{C}}^{-1}$.

An iron sphere should just pass through a circular brass ring. At $20° \mathrm{C}$, the diameter of the sphere is $25 \mathrm{cm}$ and the internal diameter of the ring is $24.9 \mathrm{cm}$. At what temperature, will the sphere just pass through the ring when both are heated together? $\alpha$ for iron $=1.2\times {10}^{-5}°{\mathrm{C}}^{-1}$ and $\alpha$ for brass $=2\times {10}^{-5}{\mathrm{per}}^{\circ }\mathrm{C}$.

A compound strip of two metals $A$ and $B$, $20 \mathrm{cm}$ Long at $15°C$ Is held horizontally with the metal $B$ Uppermost. When heated from below, the temperature of $A$ is $815°\mathrm{C}$ And of $B$ $765°\mathrm{C}$. Calculate the difference in lengths of the metal strips. $\alpha$ for $\mathrm{A}=19\times {10}^{-6}$ And for $B=12\times {10}^{-6}{/}^{\circ }\mathrm{C}$.

Two metal bars $A$ and $B$ Differ in length by $0.25 \mathrm{m}$ Whatever might be the change in temperature. If their co-efficients of linear expansion are $1.28\times {10}^{-5}$ and $1.92\times {10}^{-5}\mathrm{per}{ }^{\circ }\mathrm{C}$ Respectively, calculate the lengths of $A$ and $B$ at $0°\mathrm{C}$?

A steel metre scale is to be graduated so that the millimetre divisions are accurate within about $5\times {10}^{-5}\mathrm{mm}$ at a certain temperature. What is the maximum temperature variation allowable during the graduation? $\alpha$ for steel$=1.1\times {10}^{-5}°{\mathrm{C}}^{-1}$.

A steel scale is correct at $5°\mathrm{C}$. The length of a brass rod measured by the steel tape at $50°\mathrm{C}$ is found to be $1.5$ metre. What is the length of the rod at $100°\mathrm{C}$? $\alpha$ for steel $=11.2\times {10}^{-6}\mathrm{per}{ }^{\circ }\mathrm{C}$ and for brass $=18\times {10}^{-6}\mathrm{per}{ }^{\circ }\mathrm{C}$.