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Question
A steel rod (Y = 2.0 × 1011 Nm–2; and α = 10–50 C–1) of length 1 m and area of cross-section 1 cm2 is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?
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Solution
`L_t - L_0 (1 + aΔt)`
`L_t - L_0 = L_0a xx Δt)`
`ΔL = 1 xx 10^-5 xx 200 = 2 xx 10^-3`
`Y = (FL_0)/(AΔL)`
`L_0 = 1 m`
`F = (YAΔL)/L_0`
`A = 1 cm^2 = 10^-4m^2`
`Y = 2 xx 10^11 Nm^2`
`ΔL = 2 xx 10^-3 m`
`F = (2 xx 10^11 xx 10^-4 xx 2 xx 10^3)/1`
= `4 xx 10^-7`
= `4 xx 10^4` N
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