Thermal Expansion

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 $$\alpha_ \text{brass} = \dfrac{19 \times 10^{-6}}{^\circ C}$$]