Que: Two identical circular rod of the same diameter and same length are subjected to same magnitude of axial tensile force. One of the rod is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having modulus of elasticity of 100 Gpa. Both the material are homogeneous and isotropic and the axial force causes the same amount of uniform stress in them. if the stresses developed are within the proportional limit of respective materials, then which of the following statement are correct (Gate-2007)

(a) Both rods elongate by the same amount
(b) Mild steel rod elongates more than Cast iron rod
(c) Cast iron rod elongates more than Mild steel
(d) As the stresses are equal, strain are also equal in both the rods

Ans: (c)
Explanation: Stress are equal in both materials
Length of the both rods are same
From equation of Modulus of elasticity = stress / strain  = (force * length) / (area * change in length)
here force, length and area remain same so modulus of elasticity are directly proportional to change in length
So
For Mild steel  206 ≈ 1 /  change in length
change in length for mild steel ≈ 1 / 206 ≈ 0.0048

For Cast iron  100 ≈ 1 /  change in length
change in length for Cast iron ≈ 1 / 100 ≈ 0.01
so (elongation) change in length are higher in Cast iron