Concept:
During the manufacture of synthetic fibres, the type of yarn produced depends largely on the spinning speed (take-up speed). As the spinning speed increases, the molecular chains become more oriented, resulting in improved strength and reduced elongation.
Based on the spinning speed, man-made filament yarns are generally classified as:
\[
\begin{array}{|c|c|}
\hline
Yarn Type & Typical Spinning Speed
\hline
LOY\ (\text{Low Oriented Yarn}) & \text{Low Speed}
\hline
POY\ (\text{Partially Oriented Yarn}) & 2500-4500\ \text{mpm}
\hline
MOY\ (\text{Medium Oriented Yarn}) & 4500-6000\ \text{mpm}
\hline
FOY\ (\text{Fully Oriented Yarn}) & 6000-10000\ \text{mpm or higher}
\hline
\end{array}
\]
Thus, very high spinning speeds produce Fully Oriented Yarn (FOY).
Step 1: Identify the given spinning speed.
The given spinning speed is
\[
10,000\ \text{mpm}
\]
where
\[
\text{mpm}=\text{metres per minute}.
\]
This is a very high take-up speed used in high-speed spinning processes.
Step 2: Relate the spinning speed to the yarn type.
At such a high spinning speed,
• Molecular orientation becomes nearly complete.
• The yarn develops high tensile strength.
• The yarn requires little or no additional drawing.
Therefore, the yarn produced is
\[
\boxed{\text{Fully Oriented Yarn (FOY).}}
\]
Step 3: Examine each option.
Option (A): LOY
LOY is produced at comparatively low spinning speeds and has very low molecular orientation.
\[
\boxed{\text{Incorrect}}
\]
Option (B): FOY
FOY is produced at very high spinning speeds such as
\[
6000-10000\ \text{mpm}
\]
or even higher in modern spinning systems.
\[
\boxed{\text{Correct}}
\]
Option (C): MOY
MOY possesses intermediate orientation and is produced at medium spinning speeds.
\[
\boxed{\text{Incorrect}}
\]
Option (D): POY
POY is only partially oriented and is generally produced at much lower spinning speeds.
\[
\boxed{\text{Incorrect}}
\]
Step 4: Write the final answer.
Since the spinning speed is
\[
10,000\ \text{mpm},
\]
the yarn obtained is
\[
\boxed{\text{Fully Oriented Yarn (FOY).}}
\]
Therefore,
\[
\boxed{\text{Option (B) is the correct answer.}}
\]