Question

# A load F ( in Newtons) is applied, on a wire of length 2 m having an area of cross-section 2×10−6 m2. The extension (ΔL) versus load (F) graph of wire is as shown in the figure below. Find the young's modulus of the material of wire.

A
2×1011 N/m2
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B
2×1011 N/m2
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C
3×1012 N/m2
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D
2×1013 N/m2
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Solution

## The correct option is A 2×1011 N/m2Given, Length of wire, (L)=2 m Area of cross section,(A)=2×10−6 m2 From the extension (ΔL) versus Load (F) graph given in the question: We know, Young's modulus, Y=F×LA×ΔL Since, the graph is linear in nature, we choose a point along the graph to find the young's modulus of elasticity. Let us choose point B on graph, where (ΔL)=4×10−4 m and Load applied (F)=80 N ∴Y=80×22×10−6×4×10−4 ⇒Y=2×1011 N/m2 Young's modulus of the material of wire is 2×1011 N/m2. Hence, option(a) is correct answer.

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