A body of mass 3.14 kg is suspended from one end of a non uniform wire of length 10m, such that the radius of the wire is changing uniformly from 9.8 × 10–4 m at one end to 5 × 10–4 m at the other end. Find the change in length of the wire in mm. Young’s modulus of the material of the wire is 2 × 1011 N/m2. (mass of wire is negligible)

Engineering

Physics

Elasticity

Question

A body of mass 3.14 kg is suspended from one end of a non uniform wire of length 10m, such that the radius of the wire is changing uniformly from 9.8 × 10^–4 m at one end to 5 × 10^–4 m at the other end. Find the change in length of the wire in mm. Young’s modulus of the material of the wire is 2 × 10¹¹ N/m². (mass of wire is negligible)

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$Y = \frac{F / A}{dy / dx}, r = b - (\frac{b - a}{L}) x$

$r = b - tanθx, A = π (b - xtanθ)^{2}$

$\int_{0}^{ΔL} dy = \frac{F}{πY} \int_{0}^{L} \frac{dx}{(b - xtanθ)^{2}}$

$ΔL = 10^{- 3} m = 1 mm$

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