Concept:
Synthetic fibres are generally manufactured as continuous filaments. When these filaments are cut into short lengths suitable for spinning, they are called staple fibres.
A staple fibre is characterized by two important parameters:
• Denier (D): It indicates the fineness of the fibre.
• Cut Length (mm): It represents the length of the staple fibre.
Denier is defined as
\[
\boxed{
\text{Denier}=\frac{\text{Weight (g) of }9000\text{ m of fibre}}{}
}
\]
A lower denier indicates a finer fibre, whereas a higher denier indicates a coarser fibre.
For cotton spinning systems, the most commonly manufactured synthetic staple fibre is
\[
\boxed{1.5\text{D} \times 38\text{ mm}.}
\]
This specification provides a good balance between spinnability, strength, and yarn quality.
Step 1: Understand the significance of denier and cut length.
The denier determines the fineness of the fibre.
\[
\begin{aligned}
1.2\text{D} &\rightarrow \text{Very fine fibre},
1.5\text{D} &\rightarrow \text{Standard apparel fibre},
2.0\text{D} &\rightarrow \text{Coarser fibre.}
\end{aligned}
\]
Similarly, the cut length influences the spinning system.
A cut length of
\[
38\text{ mm}
\]
is widely used for cotton spinning machinery.
Step 2: Recall the standard commercial staple fibre specification.
In textile industries, polyester and viscose staple fibres are commonly produced in the standard specification
\[
\boxed{
1.5\text{D} \times 38\text{ mm}.
}
\]
This size is preferred because it offers
• Good fibre cohesion,
• Smooth drafting,
• Better yarn strength,
• Compatibility with cotton spinning systems.
Hence, it is regarded as the most common staple fibre specification.
Step 3: Examine each option.
Option (A): \(1.2\text{D} \times 38\text{ mm}\)
This is finer than the standard commercial staple fibre and is used for specialized applications.
\[
\boxed{\text{Incorrect}}
\]
Option (B): \(1.5\text{D} \times 38\text{ mm}\)
This is the most commonly manufactured staple fibre specification used in synthetic fibre production.
\[
\boxed{\text{Correct}}
\]
Option (C): \(2\text{D} \times 38\text{ mm}\)
This is comparatively coarser and generally used for technical or industrial applications.
\[
\boxed{\text{Incorrect}}
\]
Option (D): \(1.4\text{D} \times 38\text{ mm}\)
Although available for certain applications, it is not the standard commercial staple fibre specification.
\[
\boxed{\text{Incorrect}}
\]
Step 4: Write the final answer.
Therefore, the common type of staple fibre produced during synthetic fibre manufacture is
\[
\boxed{
1.5\text{D} \times 38\text{ mm}.
}
\]
Hence,
\[
\boxed{\text{Option (B) is the correct answer.}}
\]