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Question

A weight of 100 N is suspended by two wires made of steel and copper as shown in the figure. Length of steel wire is 1 m and copper wire is 3 m. Find the ratio of change in length of copper wire (Δlc) to change in length of steel wire (Δls). Given Young's modulus: Ysteel=2×1011 N/m2, Ycopper=1×1011 N/m2

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Solution

ΔlcΔls=?
As, Stress =FA=YΔll
Δl=FA×lY
Δlc=FcAc×lcYc--- (1)
Δls=FsAs×lsYs------(2)
As area is same so As=Ac=A
Dividing equation (1) by equation (2)
ΔlcΔls=Fc×lc×YsFs×ls×Yc

In the above expression, we don't know the ratio of forces. So,

Equating horizontal component of the two tension forces, we get
Tscos600=TCcos300
Ts2=TC32
TcTs=13
ΔlcΔls=13×31×2×10111×1011=2


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