Question
Question: Conversion of I to II:...
Conversion of I to II:

takes place by SN1
takes place by SN2
takes place both by SN1 and SN2
does not take place
takes place by SN1
Solution
The conversion of 9-bromotriptycene to 9-hydroxytriptycene involves nucleophilic substitution at the bridgehead carbon. Both SN1 and SN2 mechanisms are highly unfavorable at the bridgehead position of triptycene due to the rigidity of the structure.
The SN1 mechanism is disfavored due to the instability of the planar bridgehead carbocation. The SN2 mechanism is disfavored due to severe steric hindrance to backside attack by the nucleophile.
However, if the reaction does occur, the SN1 mechanism is generally considered less unfavorable than the SN2 mechanism at a bridgehead in rigid systems like triptycene, despite the instability of the carbocation. This is because the steric hindrance to SN2 is extremely high.