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  $\alpha _{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$

Expansion during heating

A steel rod with ${y}=2.0 \times 10^{11} \,{Nm}^{-2}$ and $\alpha=10^{-5}{ }^{\circ} {C}^{-1}$ of length $4\, {m}$ and area of cross-section $10\, {cm}^{2}$ is heated from $0^{\circ} {C}$ to $400^{\circ} {C}$ without being allowed to extend. The tension produced in the rod is ${x} \times 10^{5} \, {N}$ where the value of ${x}$ is ……. .

A metallic rod $1\,cm$ long with a square cross-section is heated through $1^o C$. If Young’s modulus of elasticity of the metal is $E$ and the mean coefficient of linear expansion is $\alpha$ per degree Celsius, then the compressional force required to prevent the rod from expanding along its length is :(Neglect the change of cross-sectional area)

The apparent coefficient of expansion of a liquid when heated in a brass vessel is $X$ and when heated in a tin vessel is $Y$. If $\alpha$ is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is ……….