3. A wire 10m long of area of cross section 1.22cm2 elongates by 1.5 cm when 4.5 kg is suspended from it. Find the (i) stress (ii) strain and (iii) young's modulus of the wire. (g = 9.8m s-2)
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Explanation:
Given, length of wire, l = 2m
cross sectional area , A = 10^-4 m²
Load , F = 102kgwt = 102 × 9.8 N
extension of wire, ∆l = 0.1cm = 0.001m
Longitudinal stress = F/A
= 102 × 9.8/(10^-4)
= 999.6 × 10^4 ≈ 1 × 10^7 N/m²
Longitudinal strain. = extension of wire/original length of wire = ∆l/l
= 10^-3/2 = 5 × 10^-4
we know, Young's modulus = longitudinal stress/longitudinal strain
= 1 × 10^7/5 × 10^-4
= 20 × 10^9 N/m²
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