$A$ clock which keeps correct time at $20\,^{\circ}C$ has a pendulum rod made of brass. How many seconds will it gain or lose per day when the temperature falls to $0\,^{\circ}C$? $(\alpha = 18 \times 10^{-6}/^{\circ}C)$

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

When the temperature of a metal sphere is increased by $40^{\circ}C$,its volume increases by $0.24\%$. The coefficient of linear expansion of the metal is ....... $^{\circ}C^{-1}$.

The scale on a steel metre stick is calibrated at $20^{\circ}C$. The error in the reading of $50 \, cm$ at $30^{\circ}C$ is: (take linear expansion coefficient of steel $\alpha = 1.0 \times 10^{-5} / ^{\circ}C$)

$A$ rod is found to be $0.05 \ cm$ longer at $40^{\circ} C$ than it is at $10^{\circ} C$. The length of the rod at $0^{\circ} C$ is (coefficient of linear expansion of the material of the rod $= 1.5 \times 10^{-5} \ {}^{\circ} C^{-1}$) (in $cm$)

At a certain temperature,rod $A$ and rod $B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_A / L_B$ is given by