A steel wire, 2mm in diameter, is just stretched between two fixed points at a temperature of `30^@C` . Determine its tension when the temperature falls to `20^@C` . (Coefficient of linear expansion of steel = `0.000011//""^@C`, Young's modulus for steel =` 2.0xx10^11Nm^(-2))`

Explanation

Thermal stress ` = F/A = Y alpha Delta t `
Tension in the wire ` = Y alpha A (t_2 - t_1)`
Here `Y = 2.0 xx 10^11 Nm^(-2), alpha = 11 xx 10^(-6) //""^@C, t_2 = 30^@C, t_1 = 20^@C, ` radius = 1mm ` = 1 xx 10^(-3) m, `
`A = pi r^2 = pi (1 xx 10^(-3))^2 = pi xx 10^(-6) m^2`
The tension in the wire
` = 2.0 xx 10^11 xx 11 xx 10^(-6) xx pi xx 10^(-6) xx (30 - 20) = 69.14N`