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
Let, Linear density of single yarn=N1 (Direct count)

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

Value of X=?


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


i.e. , Tenacity is directly proportional to breaking load(L) and inversaly proportional to linear density(N).
\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




X=2.2 (Answer)

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