Two wires of different materials, each 2m long and of diameter 2mm, are joined in series to form a composite wire. What force will produce a total length of 0.9 mm. Given Young's modulus of both wires is (Y1=2×1011pa) and (Y2=6×1011 Pa)
Given.
Length of both wires, L=2m
Radius of both wires, r=1mm=1×10−3m
Total extension of joined wire, ΔLnet=0.9mm=9×10−4m
Both wire join in series, so tension in both is equal
T=Y1AΔL1L=Y2AΔL2L
Net extension in joined wire.
⇒ΔLnet=ΔL1+ΔL2=TLY1A+TLY2A=TLA(1Y1+1Y2)
⇒ΔLnet=TLA(1Y1+1Y2)
⇒T=AΔLnetL(1Y1+1Y2)=π(10−3)2×9×10−42(12×1011+16×1011)=212.05 N
Total force produced in joined wire is 212 N