The area of a circular copper coin increases by $0.4 \%$ when its temperature is raised by $100^{\circ} C$. The coefficient of linear expansion of the coin is:

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.

$A$ uniform rod of length $L$ pivoted at one end $P$ is freely rotated in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through $P$. If the temperature of the system is increased by $\Delta T$, the angular velocity becomes $\frac{\omega}{2}$. If the coefficient of linear expansion of the rod is $\alpha$ (where $\alpha \ll 1$), then $\Delta T$ will be:

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?

$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.