A bar of iron is $10\, cm$ at $20°C$. At $19°C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/°C$)

The coefficient of linear expansion of crystal in one direction is ${\alpha _1}$ and that in every direction perpendicular to it is ${\alpha _2}$. The coefficient of cubical expansion is

If on heating liquid through $80°C$, the mass expelled is $(1/100)^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is

The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40°C$. The coefficient of linear expansion of the metal is .......... $°C$

Consider two thermometers $T_1$ and $T_2$ of equal length, which can be used to measure temperature over the range $\theta_1$ to $\theta_2$. $T_1$ contains mercury as the thermometric liquid, while $T_2$ contains bromine. The volumes of the two liquids are the same at the temperature $\theta_1$. The volumetric coefficients of expansion of mercury and bromine are $18 \times 10^{-5} \,K ^{-1}$ and $108 \times 10^{-5} \,K ^{-1}$, respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are $d_1$ and $d_2$, respectively. Then, the ratio of $d_1: d_2$ would be closest to