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Question

Copper of fixed volume V is drawn into a wire of length L. When this wire is subjected to a constant force F, the extension produced in the wire is ΔL. Which of the following graphs is a straight line?

A
ΔL versus 1L
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B
ΔL versus L2
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C
ΔL versus 1L2
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D
ΔL versus L
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Solution

The correct option is B ΔL versus L2
We know that, Young's modulus (Y)
Y=FLAΔL ...(1)
Volume, V=AL ...(2)
Eq.(1) can be written as,
Y=FL2ALΔL

From Eq.(1) and Eq.(2),
ΔL=FL2VY ...(3)
[Here, F,V and Y are constant, therefore FVY is constant]
ΔLL2

On comparing Eq.(3) with the equation of a straight line y=mx+c,
y=ΔL, c=0
Slope, m=FVY=constant
& x=L2
ΔL versus L2 graph is of the form y=mx.

Hence, ΔL versus L2 graph is a straight line passing through origin.

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