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Mechanical Properties Of Solids

Question

A steel wire of 1 m long and l mm² cross-section area is hanged from rigid end when weight of 1 kg is hang from it, then change in length will be
(Young's coefficient for wire Y = 2 x 10¹¹ N/m² )

0.5 mm

0.25 mm

0.05 mm

5 mm

Solution

0.05 mm

Young's coefficient of elasticity

Given m = 1 kg = 1000 g

Area of cross section 1 mm² = 10^-6 m²

G Y = $\frac{m g L}{π r^{2} ∆ L}$

ΔL = $\frac{m g L}{π r^{2} Y}$

= $\frac{10^{3} \times 10 \times 1}{10^{- 6} \times 2 \times 10^{11}}$

= 5 × 10^-2

Δ L = 0.05 mm