An aluminium wire and a steel wire of the same length and cross-section are joined end to end. The composite wire is hund from a rigid support and a load is suspended from the free end. If the increase in the length of the composite wire is 2.7mm, find the increase in the length of each wire.
`(Y_(Al)=0.7xx10^(11)Nm^(-2), Y_("steel")=2xx10^(11)Nm^(-2))`

Explanation

Total increase in length `,e = e_2 + e_2`
`e_1 + e_2 = 2.7 mm` . we know ` e = (FL)/(AY)`
As F,A, L are same for both the wires . So `e prop 1/Y`
`e_1/e_2 = Y_2/Y_1 = (2 xx 10^11)/(7 xx 10^11) = 20/7 , e_1 = 20/7 e_2`
substituting in `e_1 + e_2 = 2.7 mm`
`20/7 e_2 + e_2 = 2.7 mm , (27 e_2)/(7) = 2.7 mm`
` e_2 = 0.7mm , e_1 = 20/7 e_2 = 20/7 xx 0.7 = 2.0 mm`