A copper wire was subjected to a tensile stress of 7.7 x 10$^7$. Calculate the strain of the wire. [Young modules = 1.1 x 10$^11$ Nm$^{-2}$]

Analyze the question

We are given the tensile stress and Young's modulus and asked to find the strain.

Concept

Young's modulus is the ratio of stress to strain:

E = stress / strain, so strain = stress / E

Strain has no unit because it is a ratio of two lengths (extension ÷ original length).

Solution

• Stress = 7.7 × 10⁷ N/m²
• Young's modulus, E = 1.1 × 10¹¹ N/m²

Strain = (7.7 × 10⁷) / (1.1 × 10¹¹)

Strain = (7.7 / 1.1) × 10^(7 − 11)

Strain = 7.0 × 10⁻⁴

Answer

The strain is 7.0 × 10⁻⁴, which matches option C.

Tip

Always rearrange first: strain = stress ÷ E. Then divide the numbers and subtract the powers of 10 (top minus bottom). Here 7.7 ÷ 1.1 = 7 exactly, so the numbers are easy to check. Be careful not to get the power wrong, because options A to D are often built around common slips like 10⁻³ or 10⁻⁵.