A metallic wire has a Young's modulus of 2.0 10¹¹ N m ⁻² and a Poisson's ratio of 0.3 . When the wire is subjected to a stretching force, the elastic potential energy density stored in it is 4.0 10^5 J m ⁻³ . If the percentage decrease in t

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A metallic wire has a Young's modulus of 2.0 10¹¹ N m ⁻² and a Poisson's ratio of 0.3 . When the wire is subjected to a stretching force, the elastic potential energy density stored in it is 4.0 10^5 J m ⁻³ . If the percentage decrease in the diameter of the wire is x 10⁻² % , the value of x is _______.

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Correct answer: 6

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 Poisson's ratio, = _t _l Transverse strain, _t = _l = 0.3 2.0 10⁻³ = 6.0 10⁻⁴ Percentage decrease in diameter = _t 100 = 6.0 10⁻⁴ 100 = 6.0 10⁻² % Thus, x = 6 . Answer: 6

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