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 $=18\times {10}^{-6}\mathrm{per}{ }^{\circ }\mathrm{C}$.

The two ends of a steel rod of cross-section $2 {\mathrm{cm}}^2$ are rigidly fixed and its temperature is raised from $0°\mathrm{C}$ to $20°\mathrm{C}$. Calculate the thermal stress and the total force developed along the length of the rod, $\alpha$ for steel $=1.1\times {10}^{-5}\mathrm{per}{ }^{\circ }\mathrm{C}$ and $Y=2.2\times {10}^{12}$ dynes ${\mathrm{cm}}^{-2}$.

The diameter of a wheel is $0.5 \mathrm{m}$. A steel tyre of internal diameter $0.498 \mathrm{m}$ is put on the wheel. What force per unit area will the tyre exert on the wheel when it cools? $Y$ for steel $=2.1\times {10}^{11}\mathrm{N} {\mathrm{m}}^{-2}$.

A second’s pendulum keeps correct time at $20°\mathrm{C}$. It goes slow by $30$ seconds in a day at a time. What was the temperature at that time? $\alpha$ for the material of the pendulum rod$=18\times {10}^{-6}°{\mathrm{C}}^{-1}$.

A steel wire of length $8 \mathrm{m}$ and diameter $4 \mathrm{mm}$ is tied between two rigid pillars. The wire is taut. Calculate the increase of tension when the temperature of the wire is reduced by $10°\mathrm{C}$. $\alpha$ for steel $=1.2\times {10}^{-5}\mathrm{per}{ }^{\circ }\mathrm{C}$ and $Y=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$.