Question

For a wool fibre strand, the relationship between \( V_r \) (limit CV % of linear density) and \( N \) (average number of fibres in the cross-section of the strand) is given below. \[ V_r = \frac{112}{\sqrt{N}} \] For the above relationship, the CV % of linear density of wool fibre (rounded off to 2 decimal places) is ______________.

Hint:

The CV % of linear density is inversely proportional to the square root of the average number of fibres in the cross-section.

Answer 1

Correct Answer: 50.2

We are given the relationship between the CV% of linear density \( V_r \) and the average number of fibres \( N \):
\[ V_r = \frac{112}{\sqrt{N}} \] To find the CV % for wool fibre, we need to know the value of \( N \). Since \( N \) is not provided, we assume a typical value for wool fibres, say \( N = 10 \).
Substitute \( N = 10 \) into the equation: \[ V_r = \frac{112}{\sqrt{10}} = \frac{112}{3.1623} = 35.40 \] Thus, the CV % of linear density is 35.40%.
Final Answer: 35.40