In a vertical $U-$tube containing a liquid, the two arms are maintained at different temperatures ${t_1}$ and ${t_2}$. The liquid columns in the two arms have heights ${l_1}$ and ${l_2}$ respectively. The coefficient of volume expansion of the liquid is equal to

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

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 .......... $°C$

The density of water at $20^oC$ is $0.998\  gm/cm^3$ and at $40^oC$ is $0.992\ gm/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is

We are able to squeeze snow and make balls out of it because of

A steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$, percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}{ }^{\circ} C ^{-1}\right]$