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))

An aluminium wire and a steel wire of the same length and cross-sectio

1.	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))
Answer» Solution :Total increase in LENGTH, `e=e_(1)+e_(2)`. `e_(1)+e_(2)=2.7"mmwe 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))=(2xx10^(11))/(7xx10^(11))=(20)/(7), e_(1)=(20)/(7)e_(2)` substituting in `e_(1)+e_(2)=2.7`mm `(20)/(7)e_(2)+e_(2)=2.7mm, (27e_(2))/(7)=2.7`mm `e_(2)=0.7mm, e_(1)=(20)/(7)e_(2)=(20)/(7)xx0.7=2.0`mm