If the volume of a block of metal changes by $0.12 \%$ when it is heated thrugh $20^oC$, the coefficient of linear expansion (in $^oC^{-1}$) of the metal is

A rail track made of steel having length $10\,m$ is clamped on a railway line at its two ends as shown in figure. On a summer day due to rise in temperature by $20\,^oC$ , it is deformed as shown in figure. Find $x$ (displacement of the centre) if  $\alpha _{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$

A simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has time period $2s$ at  $T = 0\,^oC$ . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope $S$. If the coefficient of linear expansion of metal is $\alpha $ then the value of  $S$ is

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 $\alpha_{copper}$  = $17 \times {10^{ - 6}}per\,^\circ C$)

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)

The freezing point of the liquid decreases when pressure is increased, if the liquid