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A steel rod (Young's modulus Y = 2.0 * 10¹¹ N/m², linear expansion coefficient alpha = 10⁻⁵ per deg C) of length 4 m and cross-sectional area 10 cm² is heated from 0 deg C to 400 deg C while its ends are clamped so it cannot expand. The tension produced is x * 10⁵ N. Find x.

1. 4
2. 6
3. 8
4. 10

Correct answer: 8

Solution

Thermal tension F = Y*alpha*dT*A = 2.0*10¹¹ * 10⁻⁵ * 400 * 10*10⁻⁴ = 8*10⁵ N, so x = 8.

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