A cylindrical wire is stretched by an external force such that the elastic potential energy density stored in it becomes 4.0 10^5 J m ⁻³ . The Young's modulus and Poisson's ratio of the material of the wire are 2.0 10¹¹ N m ⁻² and 0.3 respe

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A cylindrical wire is stretched by an external force such that the elastic potential energy density stored in it becomes 4.0 10^5 J m ⁻³ . The Young's modulus and Poisson's ratio of the material of the wire are 2.0 10¹¹ N m ⁻² and 0.3 respectively. If the fractional change in the volume of the wire is x 10⁻⁴ , the value of x is _______.

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Correct answer: 8

Elastic potential energy density, u = 1 2 Y _l^2 4.0 10^5 = 1 2 2.0 10¹¹ _l^2 _l^2 = 4.0 10⁻⁶ _l = 2.0 10⁻³ The fractional change in volume of a stretched cylindrical wire is given by: V V = _l (1 - 2 ) V V = 2.0 10⁻³ (1 - 2 0.3) V V = 2.0 10⁻³ 0.4 = 0.8 10⁻³ = 8.0 10⁻⁴ Thus, x = 8 . Answer: 8

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