Coefficient of linear expansion of a vessel completely filled with $Hg$ is $1 \times 10^{-5} /{ }^{\circ} C$. If there is no overflow of $Hg$ on heating the vessel, then coefficient of cubical expansion of $Hg$ is ......

A uniform metal rod is used as a bar pendulum. If the room temperature rises by $10°C$, and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{-6}$ per $°C,$ the period of the pendulum will have percentage increase of

Two metal strips that constitute a thermostat must necessarily differ in their

The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperatures $T_1$ and $T_2$. The variation shown suggests that

The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \,K ^{-1}$. The fractional change in the density on a $30^{\circ} C$ rise in temperature is ..........

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