Question

The constant used for conversion from Denier to Cotton system is

• A. \(4315\)
• B. \(2315\)
• C. \(5315\)
• D. \(6315\)

Hint:

Remember the most important yarn count conversion formulas: \[ \boxed{ Ne=\frac{5315}{\text{Denier}} } \] and \[ \boxed{ \text{Denier}\times Ne=5315. } \] Also remember: \[ \begin{aligned} \text{Denier} &\rightarrow \text{Direct Count System} \text{Cotton Count (Ne)} &\rightarrow \text{Indirect Count System} \end{aligned} \] These conversion formulas are among the most frequently asked objective questions in Textile Technology and Spinning examinations.

Answer 1

The Correct Option is A

Concept: Different yarn numbering systems are used in the textile industry depending on the type of fibre and the spinning system. The two most common systems are:
• Denier System (Direct System)
• Cotton Count or English Count (Indirect System) In the Denier System, the yarn count is defined as the weight in grams of \(9000\) metres of yarn. \[ \boxed{ \text{Denier}=\frac{\text{Weight (g) of }9000\text{ m}}{} } \] In the Cotton Count (Ne), the count is defined as the number of \(840\)-yard hanks per pound of yarn. \[ \boxed{ Ne=\frac{\text{Number of }840\text{-yard hanks}}{\text{Weight in pounds}} } \] Since these systems are based on different units, a conversion constant is required.

Step 1: Recall the conversion formula.
The standard relationship between Denier and Cotton Count is \[ \boxed{ Ne=\frac{5315}{\text{Denier}} } \] or equivalently, \[ \boxed{ \text{Denier}\times Ne=5315. } \] Thus, the conversion constant between the Denier system and the Cotton count system is \[ \boxed{5315.} \]

Step 2: Compare with the given options.
Among the given values, \[ \begin{aligned} 4315 &\quad \text{Not the conversion constant} 2315 &\quad \text{Incorrect} 5315 &\quad \text{Standard conversion constant} 6315 &\quad \text{Incorrect} \end{aligned} \] Hence, the standard conversion constant is \[ \boxed{5315.} \]

Step 3: Identify the correct option.
The numerical value obtained corresponds to \[ \boxed{\text{Option (C).}} \]

Step 4: Final Answer.
Therefore, the constant used for conversion from Denier to Cotton system is \[ \boxed{5315.} \] Hence, \[ \boxed{\text{Option (C) is the correct answer.}} \]