GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/53

Question 53 (Textile Technology & Fibre Science)

The breaking load of a cotton yarn, with a twist multiplier of 4 tpi.Ne^-0.5, is 2.5 N. If the twist (number of turns per inch) of yarn is 20, then the tenacity (cN/tex) of the yarn (rounded off to 2 decimal places) is ____.

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

[Show Answer]

Given in the question-

$Twist multiplier=4 tpi.Ne^-0.5$

The breaking load of cotton yarn=2.5N
=2.5 x 100 cN
=250 cN

TPI=20

Tenacity of the yarn(cN/tex)=?

By formula-

$TPI=TM\times\sqrt{Count}$

$20=4\times\sqrt{Count}$

$5=\sqrt{Count}$

By doing both side square-

$5^2=(\sqrt{Count})^2$

$25=Count$

Count=25s Ne

We know-

Tex=590.5/Ne

Tex=590.5/25

Tex=23.6

Now ,by applying formula-

$Tenacity(cN/Tex)=\frac{Breaking load}{Linear density(Tex)}$

$Tenacity(cN/Tex)=\frac{250}{23.6}$

$Tenacity(cN/Tex)=10.59$ (Ans)

Previous Question

Next Question

Frequently Asked Questions | FAQs

What is breaking load ?

Breaking load, also known as maximum load or ultimate strength, is a measure of the maximum amount of force that a material can withstand before breaking or failing. This property is important in engineering and materials science as it provides information on the strength and reliability of a material in various applications. The breaking load is typically determined through a tensile test, where a sample of the material is pulled in tension until it breaks. The breaking load is usually expressed in units of force, such as Newtons or pounds-force. A high breaking load indicates that a material is strong and can resist high loads, whereas a low breaking load means that the material is weaker and may not be suitable for high-stress applications.

What is tenacity ?

Tenacity is a measure of the toughness of a material and its ability to resist breaking under stress. It is defined as the ratio of the maximum load that a material can withstand before breaking, to the original cross-sectional area of the sample. Tenacity is expressed in units of force per unit area, such as Newtons per square millimeter (N/mm²) or pounds-force per square inch (lbf/in²).
Tenacity is an important property in engineering and materials science, as it provides information on the resistance of a material to breaking or failure under different types of loads and in different applications. A material with high tenacity is considered to be tough and resistant to breaking, whereas a material with low tenacity is considered to be brittle and susceptible to breaking.
Tenacity is typically determined through a tensile test, where a sample of the material is pulled in tension until it breaks. The tenacity can also be used to compare the toughness of different materials and to determine the suitability of a material for a specific application.

GATE Textile Engineering and Fibre Science (TF) Question Papers | GATE Textile Question Answer | GATE Textile Solved Question Papers | GATE Textile Papers | GATE Textile Answer Key