Final answer:
The Young's modulus of elasticity measures a material's ability to resist deformation under stress. It can be calculated using the formula E = (F * L) / (A * ΔL). By substituting the given values, the Young's modulus of the iron bar can be determined.
Step-by-step explanation:
The Young's modulus of elasticity of a material measures its stiffness or ability to resist deformation under stress. It is defined as the ratio of stress applied to a material to the resulting strain produced.
The formula to calculate Young's modulus is: E = (F * L) / (A * ΔL), where E is the Young's modulus, F is the compressive force, L is the original length, A is the cross-sectional area, and ΔL is the change in length.
In this case, the iron bar has a length of 3 m, diameter of 13 mm (radius = 6.5 mm), and is subjected to a compressive force of 25 MN, resulting in a change in length of 5 mm. The cross-sectional area can be calculated using the formula: A = π * r^2.
By substituting the given values into the formulas, you can calculate the Young's modulus of the iron bar.