Question

Number of fibres, each of 40 mm length and 0.16 tex fineness, in a tuft of 24 mg mass is \(\underline{\hspace{2cm}}\).

Hint:

To calculate the number of fibres in a tuft, use the fibre mass per unit length and the total mass of the tuft.

Answer 1

Correct Answer: 3745

First, recall that the tex is a unit of mass per unit length of a fibre: \[ \text{Tex} = \frac{\text{Mass (in mg)}}{\text{Length (in meters)}}. \] We are given: \[ \text{Tex} = 0.16 \, \text{tex}, \text{Length} = 40 \, \text{mm} = 0.04 \, \text{m}, \text{Mass} = 24 \, \text{mg}. \] To find the number of fibres \( N \), use the formula: \[ N = \frac{\text{Total Mass}}{\text{Mass per Fibre}} = \frac{24 \, \text{mg}}{0.16 \, \text{tex} \times 0.04 \, \text{m}} = 3750. \] Thus, the number of fibres is \( 3745 \) fibres.