The ratio of linear expansion coefficient,area expansion coefficient,and volume expansion coefficient is ...............

$A$ uniform metal rod of length $L$ and mass $M$ is rotating about an axis passing through one of the ends and perpendicular to the rod with angular speed $\omega$. If the temperature increases by $t^{\circ} C$, then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod $= \alpha$)

$A$ glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is $300 \, cm^3$,then the volume of the flask is ........ $cm^3$. (Given that the coefficient of volume expansion of mercury is $\gamma_{Hg} = 1.8 \times 10^{-4} (^{\circ}C)^{-1}$ and the coefficient of linear expansion of glass is $\alpha_{glass} = 9 \times 10^{-6} (^{\circ}C)^{-1}$)

$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

The gap between any two rails, each of length $l$ laid on a railway track, is equal to $x$ at $27\,^{\circ}C$. When the temperature rises to $40\,^{\circ}C$, the gap closes up. If the coefficient of linear expansion of the material of the rail is $\alpha$, the length $l$ of a rail at $27\,^{\circ}C$ is:

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