A steel bolt of cross-sectional area `A_(b) = 5 xx 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 = 50 cm`. The bolt is just taut so that there is no stress in the bolt and temperature of the assembly increases through `/_\theta=10^@C`. Given, coefficient of linear thermal expansion of steel, `alpha_(b) = 10^(-5)//^@C`.

Young's modulus of steel `Y_(b)=2xx10^(11)N//m^(2)`
Young's modulus of `Al, Y_(t)=10^(11) N//m^(2)`, coefficient of linear thermal expansion of `Al `alpha_(t)=2xx10^(-5)//^@C`
The compressive stress in tube is

Options

A. `5xx10^(6)N//m^(2)`
B. `10^(5)N//m^(2)`
C. `10^(8)N//m^(2)`
D. `10^(3)N//m^(2)`

Answer

A

Explanation

Compressive stress in tube
`sigma_(t)=E_(t)Y_(t)=5xx10^(6)N//m^(2)`