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Question

A wire of length 1 m and radius 1mm is subjected to a load. The extension is x. The wire is melted and then drawn into a wire of square cross-section of side 1mm. What is the extension under the same load?

A
π2x
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B
πx2
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C
πx
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D
π/x
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Solution

The correct option is A π2x
Given that,
Length l=1m
Radius r=1mm
Extension =x
Cross section area of wireA=πr2=πmm2
The volume of the wire V=Al=πmm3
Now, after melting
The length of the wire l=VA=πmm

Now, we know that
Stress=strainconstant

For case first,
FA=stress
Δll=strain
Now,
F×lA×Δl=constant

Now, we have
F1×l1A1×Δl1=F2×l2A2×Δl2
1x×π=πΔl2
Δl2=π2x
Hence, the extension under the same load is π2x


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