Question

The diameter of yarn is ........... to the square roots of the cotton count.

• A. Equal
• B. Directly proportional
• C. Non-directly proportional
• D. Inversely proportional

Hint:

Always remember: Higher cotton count = finer yarn (smaller diameter). Formula: \( d \propto 1/\sqrt{N} \).

Answer 1

The Correct Option is D

Step 1: Yarn Count Explained
Yarn count indicates yarn fineness. It's the number of 840-yard hanks per pound of yarn. A higher count signifies finer yarn; a lower count means coarser yarn.
Step 2: Count and Diameter Relationship
Yarn diameter relates to yarn count via the formula: \[\text{Diameter of yarn} \propto \frac{1}{\sqrt{\text{Count}}}\] Diameter is inversely proportional to the square root of the cotton count.
Step 3: Option Evaluation
- Equal: Incorrect. - Directly proportional: Incorrect; a higher count yields finer yarn (smaller diameter). - Non-directly proportional: Vague and inaccurate. - Inversely proportional: Correct; as count increases, diameter decreases proportionally to \(1/\sqrt{\text{Count}}\).
Step 4: Conclusion
Yarn diameter is inversely proportional to the square root of the cotton count.