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The length of a metal wire is l(1) when ...

The length of a metal wire is `l_(1)` when the tension in it is `T_(1)` and is `l_(2)` when the tension is `T_(2)`. The natural length of the wire is:

Text Solution

Verified by Experts

`"From length expansion equation "(DeltaL)/(L)=alpha_(L)DeltaT`
`"From Area expansion equation, "((DeltaV)/(V_(o)))=alpha_(A)DeltaT`
But `alpha_(A)=2alpha_(L)`, therefore, `(DeltaA)/(A_(o))=2alpha_(A)DeltaT=2(DeltaL)/(L)`
Percentage change `=(DeltaA)/(A_(o))xx100=2((DeltaL)/(L)xx100)=2xx1`
Percentage change `=2%`
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Knowledge Check

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