Which ONE or MORE among the following tube cross-sections shown can be produced by true centrifugal casting method? Note: The cross-sections shown are perpendicular to the axis of rotation. Figures are not to scale.
Show Hint
Remember that in true centrifugal casting the outer shape is set by the mold but the inner bore is always a circle, since it forms from the free liquid surface.
Step 1: The One Rule That Decides Everything:
For true centrifugal casting there is a single governing rule to remember: the outer profile is controlled by the mold, but the inner profile is controlled purely by the spinning liquid itself.
Since a rotating liquid under centrifugal action always settles into a shape of constant radius, the inner bore of any true centrifugal casting must be a perfect circle.
No amount of clever mold design can force the free inner surface into a square, pentagon, or any other polygon, because there is no core touching that surface.
Step 2: Applying the Rule as a Filter:
Using this rule as a quick filter, we simply need to reject every option whose inner shape is not a circle and accept every option whose inner shape is a circle, regardless of what the outer shape looks like.
$$ \text{Inner shape is a circle} \implies \text{achievable}, \quad \text{Inner shape is not a circle} \implies \text{not achievable} $$
Step 3: Sorting the Four Options:
Option (A) has a pentagon inner bore, this fails the filter immediately.
Option (B) has an octagon outer profile with a circular inner bore, this passes the filter since only the outer shape is a polygon.
Option (C) has a pentagon outer profile with a circular inner bore, this also passes since the inner bore is still circular.
Option (D) has a circular outer profile with a circular inner bore, the simplest and most standard case, this clearly passes.
Final Answer:
Filtering by the rule that the inner bore must be circular leaves options (B), (C), and (D) as the achievable cross-sections.
\[ \boxed{\text{(B), (C), (D)}} \]
