Question

Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of a cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogenous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?

• A. Both rods elongate by the same amount
• B. Mild steel rod elongates more than the cast iron
• C. Cast iron rod elongates more than the mild steel rod
• D. As the stresses are equal strains are also equal in both the rods

Answer 1

The correct option is C Cast iron rod elongates more than the mild steel rod

Given, $E_s$ = 206 GPa and $E_c$ = 100 GPa
Elongation in mild steel,
$\Delta L_s=\frac{PL}{A{E}_s}...\left(i\right)$
Elongation in cast iron,
$\Delta L_c=\frac{PL}{A{E}_c}...\left(ii\right)$
Dividing Eq. (ii) by Eq.(i), we get
$\frac{\Delta L_s}{\Delta L_c}=\frac{E_c}{E_S}$
Since diameter and length of both shafts are equal
$\therefore \frac{\Delta L_s}{\Delta L_c}=\frac{100}{206}<1$