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A cylindrical copper rod is subjected to a longitudinal (uniaxial) compressive pressure p = 1000 kgf/cm². Taking Poisson's ratio mu = 0.34 and Young's modulus Y = 1.18 * 10¹¹ N/m² for copper, find the relative change in its density (magnitude of delta_rho / rho).

1. 2.7 * 10⁻⁴
2. 1.4 * 10⁻⁴
3. 5.3 * 10⁻⁴
4. 8.3 * 10⁻⁴

Correct answer: 2.7 * 10⁻⁴

Solution

Under uniaxial stress the fractional volume change is -(p/Y)(1 - 2mu); converting p to about 9.81*10⁷ Pa gives delta_rho/rho = (p/Y)(1 - 2mu) approximately 2.7*10⁻⁴.

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