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When a uniform cylindrical steel wire is subjected to a suitable axial force, its volume changes by 0.2% and its radius changes by 0.002%. Given Young's modulus Y = 2.0 x 10¹¹ N/m², find the longitudinal tensile stress in the wire.

1. 3.2 x 10⁹ N/m²
2. 3.2 x 10⁷ N/m²
3. 3.6 x 10⁹ N/m²
4. 3.9 x 10⁸ N/m²

Correct answer: 3.9 x 10⁸ N/m²

Solution

From dV/V = 2(dr/r) + dL/L, the longitudinal strain is dL/L = 0.2% - 2(0.002%) = 0.196%; stress = Y*strain ~ 3.9 x 10⁸ N/m².

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