If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} C$,then find its coefficient of linear expansion.

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system,

$A$ clock which keeps correct time at $20^{\circ} C$, is subjected to $40^{\circ} C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} C$, how much time will it gain or lose per day?

$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be:

The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

Each side of a cubic metal box is $a$ at room temperature $T$. The coefficient of linear expansion of the metal sheet is $\alpha$. The metal box is heated uniformly by a small temperature $\Delta T$,so that its new temperature is $T + \Delta T$. Calculate the increase in the volume of the metal box.