GATE (TF) Textile 2003 Question Paper Solution | GATE/2003/TF/62

Question 62 (Textile Engineering & Fibre Science)

A single yarn of 30 tex is converted into two ply yarn. If the ratio of tenancies of the plied and single yarn is 1.2, the ratio of their breaking strengths will be

(A)	2.0
(B)	3.0
(C)	2.4
(D)	4.0

[Show Answer]

Option C is correct.

Given-

Single yarn tex(N1)=30

Then,plied yarn tex(N2)=60

The ratio of tenancies of the plied and single yarn(T2:T1) =1.2

The ratio of their breaking strengths(S2:S1)=?

By formula-

$Tenacity(T)=\frac{breaking strength(S)}{tex(N)}$

$\frac{T_1}{T_2}=\frac{S_1}{S_2} \times \frac{N_2}{N_1}$

$\frac{1}{1.2}=\frac{S_1}{S_2} \times \frac{60}{30}$

$\frac{1}{1.2}=\frac{S_1}{S_2} \times \frac{2}{1}$

$\frac{S_1}{S_2}=\frac{1}{1.2 \times 2}$

$\frac{S_1}{S_2}=\frac{1}{2.4}$

$\frac{S_2}{S_1}=2.4$

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