### Thermal Expansion

goals
A steel bolt of cross-sectional area ${A}_{b}=5\times { 10 }^{ -5 }{ m }^{ 2 }$ is passed through a cylindrical tube made of aluminium. Cross-sectional area of the tube material is ${A}_{t}= { 10 }^{ -4 }{ m }^{ 2 }$ and its length is $l=50cm$. The bolt is just taut so that there is no stress in the bolt and temperature of the assembly increases through $\Delta \theta={10}^{o}C$. Given, coefficient of linear thermal expansion of steel, ${\alpha}_{b}={10}^{-5}/^{o}C$.
Young's modulus of steel ${ Y }_{ b }=2\times { 10 }^{ 11 }N{ m }^{ 2 }$
Young's odulus of $AI$, ${ Y }_{ t }={ 10 }^{ 11 }N{ m }^{ -2 }$, coefficient of linear thermal expansion of $AI$ ${\alpha}_{t}=2\times {10}^{-5}/^{o}C$
Solid ...... on heating and ....... on cooling
For a plate expansion in ....... is considered
When the temperature of a rod of copper is increased, its length
A cylinder steel plug is inserted into a circular hole of diameter $2.60 cm$ in a brass plate. When the plug and the plates are at a temperature of $20^\circ C$, the diameter of the plug is $0.010 cm$ smaller than that of the hole. The temperature at which the plug will just fit in it is:
[Given, $\alpha_ \text{steel} = \dfrac{11 \times 10^{-6}}{^\circ C}$ and $\alpha_ \text{brass} = \dfrac{19 \times 10^{-6}}{^\circ C}$]