two steel wires of the same radius have their lengths in the ratio 1:2 . If they are stretched by the same force then the strains produced in the two wires is in the ratio
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The ratio of strain will be 1:1
We know that the young's modulas is given by,
Y = stress / strain = (F/A) / strain
=> strain = F/AY
where,
F = force applied
A = area of cross section
since the wires are made of same material so there young's modulus will be same.
Also the force applied and the area of cross section is same(because radius is same)
Hence,
strain₁/strain₂ = F₁A₂Y₂/F₂A₁Y₁ = 1
Hence the ratio of strain will be 1:1 despite of the ratio of length.
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