The density of a substance at $0^{\circ}C$ is $10 \, g/cm^3$ and at $100^{\circ}C$,its density is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is:

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?

$A$ 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 $= 1.2 \times 10^{-5}\; K^{-1}$)

What is areal expansion? Give the definition and unit of the coefficient of areal expansion.

$A$ metal rod having a coefficient of linear expansion $2 \times 10^{-5} /{ }^{\circ} C$ is $0.75 \ m$ long at $45^{\circ} C$. When the temperature rises to $65^{\circ} C$,the increase in length of the rod will be: (in $mm$)

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,what happens to the diameters?