Answer
The following synthetic conversion can be obtained through adding a strong base (KOH) and then oxymercuration-demercuration of alkene.
Work Step by Step
Since we need a double bond to perform oxymercuration- demercuration, we have to first make alkene from 1-iodo-2-methylcyclopentane. The addition of KOH in presence of heat favors elimination to give an alkene. Then oxymercuration- demercuration is performed with the following steps:
1) Electrophilic attack of $ ^+Hg(OAc)$ forms a mercurinium ion.
2) $OH^-$ attacks the most substituted carbon and opens the ring to give an organomercurial alcohol.
3) Demercuration with $NaBH_4$ replaces the mercuric fragment with hydrogen to give an alcohol.