A rubber string 10 m long is suspended from a rigid support at it… - Vidyadip

Question

A rubber string 10 m long is suspended from a rigid support at its one end. Calculate the extension in the string due to its own weight. The density of rubber is $1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}$ and Young's modulus for the rubber is $5 \times 100 \mathrm{~N} / \mathrm{m}^2$. The breaking stress for a metal is $7.8 \times 10^9 \mathrm{~N} / \mathrm{m}^2$. Calculate the maximum length of the wire made of this metal with may be suspended without breaking. The density of metal $=7.8 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$.

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Answer

$\text{l}=10\text{m}.\rho=1.5\times10^3\text{kg/m}^3$ $\text{Y}=5\times10^6\text{N/m}^2$ We know, $\text{Y}=\frac{\text{F}.\text{l}}{\text{A}.\Delta\text{l}}$ Eficient force = Mg Consider a small length dy at a distance y from free end. The length above this, (l - y) will experience a force of $\text{F}_{\text{dx}}=\frac{\text{M}}{\text{l}}(\text{dy}).\text{gdy}$

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