###### 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=**T _{1}**

Then, tenacity of two-fold yarn(

**T**)=

_{2}**1.1T**

_{1}Let, Breaking load of single yarn=

**L**

_{1}Then , Breaking load of two fold component yarn(

**L**)=

_{2}**XL**

_{1}and

Let, Linear density of single yarn=

**N**(Direct count)

_{1 }Then ,Linear density of two-fold yarn(

**N**)=

_{2}**2N**

_{1}Value of

**X**=

**?**

**Formula**:

i.e. ,

**Tenacity is directly proportional to breaking load(L) and inversaly proportional to linear density(N)**.

Then,

As given in the question-

**X=**2.2

**(Answer)**