A steel wire, 2mm in diameter, is just stretchedbetween two fixedpointsat a temperatureof 30^(0)C. Determineits tensionwhenthe temperaturefalls to 20^(0)C. (Coefficient of linearexpansionof steel =0.000011//""^(0)C, Young.s modulusfor steel=2.0xx10^(11)Nm^(-2))

A steel wire, 2mm in diameter, is just stretchedbetween two fixedpoint

1.	A steel wire, 2mm in diameter, is just stretchedbetween two fixedpointsat a temperatureof 30^(0)C. Determineits tensionwhenthe temperaturefalls to 20^(0)C. (Coefficient of linearexpansionof steel =0.000011//""^(0)C, Young.s modulusfor steel=2.0xx10^(11)Nm^(-2))
Answer» Solution :Theremalstress`=(F)/(A) =Y alpha Delta t` Tensionin the wire`=Y alpha A(t_(2)-t_(1))`. Here,`Y=2.0xx10^(11)Nm^(-2) , alpha =11xx10^(-6) //""^(0)C`, `t_(2) =30^(0)C, t_(1) =20^(0)C, `radius = 1mm `=1xx10^(-3)m`, `A=pi r^(2)=pi(1xx10^(-3))^(2) = pi xx 10^(-6) m^(2) ` The tensionin the wire `=2.0xx10^(11) xx11 xx 10^(-6) xx pi xx 10^(-6) xx (30-20)=69.14 N`