In strength of materials, the modulus of elasticity (Young modulus) for mild steel is approximately equal to which of the following values?

Introduction / Context:
The modulus of elasticity, also called Young modulus, is a fundamental property of materials that measures their stiffness. It relates stress to strain within the elastic range of deformation. Mild steel is one of the most commonly used structural materials in civil and mechanical engineering, so knowing its approximate modulus of elasticity is important for design calculations, deflection checks and structural analysis. This question tests your recall of the standard approximate value used for mild steel.

Given Data / Assumptions:

• We are dealing with mild steel, not high alloy steels or other metals.
• The modulus of elasticity is usually denoted by E.
• Engineering handbooks list E for mild steel as approximately 2 * 10^5 N/mm2.
• The options are expressed in kN/mm2, where 1 kN/mm2 equals 10^3 N/mm2.

Concept / Approach:
Young modulus E is defined as E = stress / strain within the linear elastic region of a material stress strain curve. For mild steel, experimental tests and standards show that E is roughly 200 to 210 gigapascals. In N/mm2, this is approximately 2 * 10^5 N/mm2. Converting to kN/mm2 simply divides by 1000, giving around 200 to 210 kN/mm2. Therefore, among the options, 210 kN/mm2 is the closest standard engineering value. Lower values such as 80 or 100 kN/mm2 would indicate a much more flexible material, and 10 kN/mm2 would be extremely low and unrealistic for steel.

Step-by-Step Solution:
Step 1: Recall that 1 gigapascal equals 10^3 N/mm2.Step 2: Remember that the typical Young modulus for mild steel is about 200 to 210 gigapascals.Step 3: Convert 200 gigapascals to N/mm2 to get 2 * 10^5 N/mm2.Step 4: Recognise that 2 * 10^5 N/mm2 equals 200 kN/mm2, and a commonly rounded design value is about 210 kN/mm2.Step 5: Examine the options and identify 210 kN/mm2 as the only value matching this standard range.Step 6: Conclude that the modulus of elasticity for mild steel is approximately 210 kN/mm2.

Verification / Alternative check:
Design codes and engineering textbooks usually quote E for structural steel or mild steel as around 2 * 10^5 N/mm2. Many example calculations such as beam deflection or column buckling use this value. If you look at comparative tables of material properties, aluminium is often listed with a much lower modulus around 70 * 10^3 N/mm2, which would be about 70 kN/mm2, while concrete has an even lower modulus. These comparisons make it clear that values like 80 kN/mm2 or 10 kN/mm2 would be inconsistent with the known stiffness of steel.

Why Other Options Are Wrong:
100 kN/mm2 is only about half the accepted stiffness of mild steel and would incorrectly predict much larger elastic deflections. 80 kN/mm2 is even lower and more typical of very flexible materials, not steel. 10 kN/mm2 is extremely small and does not match any structural metal in common use. Therefore these values cannot represent the modulus of elasticity for mild steel, while 210 kN/mm2 fits the well documented range.

Common Pitfalls:
Students sometimes mix up units when dealing with gigapascals, megapascals, N/mm2 and kN/mm2, leading to errors of a factor of 1000. Others may remember the value as 2 * 10^5 but fail to convert correctly to kN/mm2. To avoid mistakes, always check unit conversions carefully and remember that mild steel is relatively stiff, so its Young modulus should be on the order of hundreds of kN/mm2, not tens.

Final Answer:
The modulus of elasticity for mild steel is approximately 210 kN/mm2, which corresponds to about 2 * 10^5 N/mm2.