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Question

A wire of length 2 m is suspended from the top of a roof at one end and a load of W is attached at the other end. Cross-sectional area of the wire is 5×107 m2 and elongation (Δl) is shown in the graph. Find the Young's modulus of elasticity of the wire material.


A
1×1011 N/m2
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B
1.6×1012 N/m2
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C
2×1011 N/m2
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D
4×1011 N/m2
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Solution

The correct option is D 4×1011 N/m2
Young's modulus of elasticity is given by
Y=stressstrain

Note: Young's modulus is only valid till proportionality limit.
Y=FAΔll=FlAΔl
From the graph, we can see Δl=2×104 m when F=50 N
Y=20×25×107×2×104 = 4×1011 N/m2

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