$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)

Two brass rods $A$ and $B$ have lengths $l$ and $2l$ and radii $2r$ and $r$ respectively. If both are heated to the same temperature,the ratio of the increase in their volumes is:

$A$ crystal has a linear expansion coefficient of $\alpha_1$ in one direction and $\alpha_2$ in all directions perpendicular to it. What will be the volume expansion coefficient of the crystal?

Two uniform brass rods $A$ and $B$ of length $l$ and $2l$ and their radii $2r$ and $r$ respectively are heated to the same temperature. The ratio of the increase in the volume of rod $A$ to that of rod $B$ is

$A$ unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$,using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that the difference between their lengths remains constant. If the length of brass is $40\,cm$,what is the length of iron in $cm$?
($\alpha_{\text{iron}} = 1.2 \times 10^{-5} K^{-1}$ and $\alpha_{\text{brass}} = 1.8 \times 10^{-5} K^{-1}$)

Show that the coefficient of area expansion,$(\Delta A / A) / \Delta T,$ of a rectangular sheet of a solid is twice its linear expansivity,$\alpha_{l}$.