A non-isotropic solid metal cube has coefficients of linear expansion as:

$5 \times 10^{-5} /^{\circ} \mathrm{C}$ along the $\mathrm{x}$ -axis and $5 \times 10^{-6} /^{\circ} \mathrm{C}$ along the $y$ and the $z-$axis. If the coefficient of volume expansion of the solid is $\mathrm{C} \times 10^{-6} /^{\circ} \mathrm{C}$ then the value of $\mathrm{C}$ is

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 volume of the flask is …….. $cm^3$. (given that coefficient of volume expansion of mercury and coefficient of linear expansion of glass are $1.8 × 10^{-4} (^o C)^{-1}$ and $9 × 10^{-6} (^o C)^{-1}$ respectively)

A steel scale measures the length of a copper wire as $80.0\,cm,$ when both are at $20^\circ C$ (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at $40^\circ C$ $?$ (Given $\alpha_{steel} $ = $11 \times {10^{ – 6}}$per$°C$ and $\alpha_{copper}$  = $17 \times {10^{ – 6}}per\,^\circ C$)

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

An open vessel is filled completely with oil which has same coefficient of volume expansion as that of the vessel. On heating both oil and vessel,