Final answer:
A pin in a confined smooth slot allows rotation but no translation, and does not fully restrict movement like a fixed support.
Thus, the correct option is B.
Step-by-step explanation:
When analyzing support reactions for a pin in a confined smooth slot, it is important to understand the type of constraint it offers to a structure or mechanical system. The correct statement about a pin in a confined smooth slot is that it Allows rotation but no translation. This means that the pin can constraint a body in such a way that the body is not able to translate (move linearly) in the slot's plane, but it can rotate about the pin. It is not equivalent to a fixed support because a fixed support would prevent both rotation and translation entirely. The slot provides a very specific type of support which allows the pinned object some degree of freedom to rotate.
A confined smooth slot does not completely restrict movement; it mainly restricts translation in the plane perpendicular to the slot while allowing rotation. This is different from a fixed support, which would restrict all movements and provide full constraint. A pin in a confined smooth slot provides a unique support condition that is useful in various engineering applications where controlled movement is required.
Therefore, the correct option is b) Allows rotation but no translation