Question

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 = 50 cm. The bolt is just taut so that there is no stress in the bolt and temperature of the assembly increases through $\Delta \theta ={10}^{\circ }C$. Given, coefficient of linear thermal expansion of steel, ${\alpha }_b={10}^{-5}{/}^{\circ }C.$

Young's modulus of steel $Y_b=2\times {10}^{11}N/m^2.$

Young's modulus of Al, $Y_t={10}^{11}N/m^2,$ coefficient of

linear thermal expansion of Al ${\alpha }_t=2\times {10}^{-5}{/}^{\circ }C.$

The tensile stress in bolt is:

• A. ${10}^{4}N/m^2$
• B. ${10}^{7}N/m^2$
• C. $2\times {10}^{8}N/m^2$
• D. ${10}^{10}N/m^2$

Answer 1

The correct option is B ${10}^{7}N/m^2$

Tensile stress in bolt

${\sigma }_b=\frac{Y_b(\Delta l-l{\alpha }_b\Delta \theta )}{l}={10}^{7}N/m^2$