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

    

1. x22L2 2. x L
3. x2L 4. x22L
(1) Hint: Use Pythagoras theorem to find the change in length.
Step 1: Find the change in length.  
Consider the diagram below
Hence, change in length

=2BO-2BD                                  ( BO=OC, BD=DC)
=2[BO-BD]
=2x2+L212-L
=2L1+x2L212-1
=2L1+x22L2-1=x2L
Step 2: Find the strain.
Strain=LL=x22L2