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A cylindrical wire of radius 1 mm and length 1 m (Young's modulus = 2 x 10¹¹ N/m², Poisson's ratio mu = pi/10) is stretched by a force of 100 N. What does its radius become?

1. 0.99998 mm
2. 0.99999 mm
3. 0.99997 mm
4. 0.99995 mm

Correct answer: 0.99995 mm

Solution

Longitudinal strain = 100/(pi*1e-6*2e11) = 1.59e-4; Delta r/r = -(pi/10)(1.59e-4) = -5e-5, so r = 0.99995 mm.

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