A steel wire of cross section 1 mm2 is heated at `60^(@)` C and tied between two ends family. Calculate change in tension when temperature becomes `30^(@) C` coefficient of linear expansion for steel is `alpha = 1.1 xx 10 ^(-5) "”^(@)C ^(-1), Y =2 xx 10 ^(11) Pa.` (Change in length of wire due to change in temperature `(Delta t) is Delta l = alpha l Delta t)`

Explanation

Here `A = 1 mm ^(2) = 10 ^(-6) m ^(2)`
`theta _(1) = 60 ""^(@)C, theta _(2) = 30 ""^(@) C`
`therefore Delta theta = 60-30 = 30 "^(@)C`
`therefore alpha = 1.1 xx 10 ^(-5) ""^(@)C ^(-1)`
`therefore Y = 2 xx 10 ^(11) Pa`
here temperature change `= Delta theta`
Due to `Delta theta` change in temperature chang ein length of wire `(Delta l)/(l) = alpha xx Delta theta `
`=1.1 xx 10 ^(-5) xx 30 ^(@)`
`= 3.3 xx 10 ^(-4)`
Now Young.s Modulus `Y=(A )/(( Delta l )/( l ))`
`therefore F = ( YA Delta l )/(l )= 2 xx 10 ^(11) xx 10 ^(-6) xx 3.3 xx 10 ^(-4)`
`=6.6 xx 10 ^(1) `
`therefore F = 66 N`