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Q.

A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (figure ). A mass m is suspended from the mid-point of the wire. Strain in the wire is [NCERT Exemplar]

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a

x22L2

b

xL

c

x2/L

d

x2/2L

answer is A.

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Detailed Solution

Consider the diagram belowHence, change in length,  ΔL=BO+OC−(BD+DC)=2BO−2BD (∵BO=OC,BD=DC)=2[BO−BD]=2x2+L21/2−L=2L1+x2L21/2−1≈2L1+12x2L2−1=x2L(∵x<
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