GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/48

Question 48 (Textile Engineering & Fibre Science)

The tenacity of a two-fold yarn is 1.1 times the tenacity of its component single yarn. The breaking load of the two-fold yarn is X times the breaking load of its single component yarn. Neglecting length contraction due to twist, the value of X, accurate to one decimal place, is __2.1 to 2.3__.

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Given in the question–
Let, tenacity of single yarn=T₁

Then, tenacity of two-fold yarn(T₂)=1.1T₁

Let, Breaking load of single yarn=L₁

Then , Breaking load of two fold component yarn(L₂)=XL₁
and
Let, Linear density of single yarn=N₁ (Direct count)

Then ,Linear density of two-fold yarn(N₂)=2N₁

Value of X=?

Formula:

$Tenacity=\frac{Breaking load(L)}{Linear density(N)}$

$Tenacity\alpha\frac{L}{N}$

i.e. , Tenacity is directly proportional to breaking load(L) and inversaly proportional to linear density(N).
Then,
$\frac{T_1}{T_2}=\frac{L_1}{L_2}\times \frac{N_2}{N_1}$

As given in the question-

$\frac{T_1}{1.1T_1}=\frac{L_1}{XL_1}\times \frac{2N_1}{N_1}$

$\frac{1}{1.1}=\frac{1}{X}\times \frac{2}{1}$

$\frac{1}{1.1}=\frac{1}{X}\times 2$

$\frac{1}{1.1}=\frac{2}{X}$

$\frac{X}{1.1}=\frac{2}{1}$

$X=2\times1.1$

X=2.2 (Answer)

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