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A wire of length 2 m is fixed, as shown....

A wire of length 2 m is fixed, as shown. When a load is suspended from the center, it sags by 2 cm. Find the strain.

Text Solution

Verified by Experts

In right - angled triangle, `DeltaADC`
AD=1 m =100 cm = L
`DC=2` cm
`AC=L+DeltaL`
`angleD=90^(@)`
`:.` By Pythagoras theorem,
`AC^(2)+AD^(2)+DC^(2)`
`(L+DeltaL)^(2)=L^(2)|(2" cm")^(2)`
`L^(2)+2L(Delta L)+(DeltaL)^(2)=L^(2)+4" cm"^(2)`
`2L(DeltaL)=4" cm"^(2)" (neglecting "DeltaL^(2))`
`DeltaL=(4" cm"^(2))/(2L)=(4" cm"^(2))/(2xx100" cm"=0.02" cm"`
Strain `=(DeltaL)/(L)=(0.02" cm")/("100 cm")=2xx10^(-4)=0.0002`
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