GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/50

Question 50 (Textile Technology & Fibre Science)

The tensile load $(F)$ in Newton $(N)$ and the elongation $(\varepsilon)$ in cm of a yarn are related as follows

$F=2\varepsilon^2 + \varepsilon$

If the breaking elongation of the yarn is 10 cm, then the work of rupture (N.m) of yarn (rounded off to 2 decimal places) is ____.

(A)
(B)
(C)
(D)

[Show Answer]

Given in the question-

Breaking elongation of the yarn( $\varepsilon$ ) =10 cm

The work of rupture (N.m) of the yarn=?

Given-

$Tensile load(F)=2\varepsilon^2 + \varepsilon$

The work of rupture is the area plotted between tensile load and breaking elongation(Interation).

So,
$The work of rupture=\int_{0}^{10} (2\varepsilon^2 + \varepsilon) d \varepsilon$

$The work of rupture=\int_{0}^{10}2\varepsilon^2 d \varepsilon+\int_{0}^{10} \varepsilon d \varepsilon$

$The work of rupture=2\int_{0}^{10}\varepsilon^2 d \varepsilon +\int_{0}^{10} \varepsilon d \varepsilon$

$The work of rupture=2[\frac{\varepsilon^3}{3}]_{0}^{10} +[\frac{\varepsilon^2}{2}]_{0}^{10}$

$The work of rupture=2[\frac{10^3}{3}-\frac{0^3}{3}]+[\frac{10^2}{2}-\frac{0^2}{2}]$

$The work of rupture=2[\frac{1000}{3}]+[\frac{100}{2}]$

$The work of rupture=[\frac{2000}{3}]+[\frac{100}{2}]$

$The work of rupture=666.7+50$

$The work of rupture=716.7$ N.cm

$The work of rupture=7.167$ N.m

$The work of rupture=7.17$ N.m (Ans)

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Frequently Asked Questions | FAQs

What is breaking elongation ?

Breaking elongation refers to the amount of elongation or stretching that a material undergoes before it breaks or fails. This property is important in engineering and materials science as it helps to predict the behavior of materials under stress and how they will perform in various applications. The breaking elongation is usually expressed as a percentage of the original length of the material and is measured after a tensile test, where a sample of the material is pulled until it breaks. A high breaking elongation indicates that the material is more flexible and ductile, whereas a low breaking elongation means that the material is stiff and brittle.

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