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A steel wire with a cross-sectional area...

A steel wire with a cross-sectional area `0.4mm^(2)` is fixed tightly at `20^(@)C` between two rigid supports. If the temperature falls to `0^(@)C`, what will be the tension on the string? Given, for steel, Y `=2 times 10^(12)dyn*cm^(-2) " and " alpha=12 times 10^(-6@)C^(-1).`

Text Solution

Verified by Experts

The tension developed `=YAalphat`
A = area of cross-section = 0.5 `mm^(2)=0.004 cm^(2)`
Y = Young.s modulus `=2 times 10^(12)dyn*cm^(-2)`
`alpha` = coefficient of linear expansion `=12 times 10^(-6@)C^(-1)`
t = fall in temperature = 20 - 0 = `20^(@)C`
`therefore` Tension developed
`=2 times 10^(12) times 0.004 times 12 times 10^(-6) times 20`
`=19.2 times 10^(5)dyn.`
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