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A steel rod (Y = 2.0 xx 10^(11) N//m^(2)...

A steel rod `(Y = 2.0 xx 10^(11) N//m^(2) " and "alpha = 10^(-50).^(@)C^(-1))` of length 1 m and area of cross-section 1 `cm^(2)` is heated from `0.^(@)C` to `200^(@)C`, without being allowed to extend or bend. What is the tension produced in the rod?

Text Solution

Verified by Experts

Given, Young's modulus of steel `Y = 2.0 xx 10^(11) N//m^(2)`
Coefficient of thermal expansion `alpha = 10^(-5). ^(@)C^(-1)`
Length l = 1 m
Area of cross-section `A = 1 cm^(2) = 1 xx 10^(-4) m^(2)`
Increase in temperature `Deltat = 200^(@)C - 0^(@)C = 200 ^(@)C`
Tension produced in steel rod (F) = `YA alpha Deltat`
`=2.0 xx 10^(11) xx1 xx 10^(-4) xx10^(-5) xx200`
`= 4 xx 10^(4) N`
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