The coefficient of area expansion of a solid is $2 \times 10^{-5} \, ^{\circ}C^{-1}$. Its coefficient of linear expansion is:

$A$ pendulum clock keeps correct time at $0\,^{\circ}C$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha$. If the temperature rises to $t\,^{\circ}C$,then the clock loses per day by (in seconds):

$A$ 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 $\alpha_{glass} = 9 \times 10^{-6} (^{\circ}C)^{-1}$)

The volume of the bulb of a mercury thermometer at $0^\circ C$ is $V_0$ and the cross-section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ per $^\circ C$ and the coefficient of cubical expansion of mercury is $\gamma_m$ per $^\circ C$. If the mercury just fills the bulb at $0^\circ C$,what is the length of the mercury column in the capillary at $T^\circ C$?

To increase the length of a metal rod by $0.4 \%$, the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

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: