Step 1: Identifying the structure.
The compound is a cyclopentane ring with a chlorine (\(\text{Cl}\)) attached to the 4th carbon, a methyl group (\(\text{CH}_3\)) attached to the 2nd carbon, and a hydroxyl group (\(\text{-OH}\)) attached to the 4th carbon. The IUPAC name should reflect the correct positions of these groups.
Step 2: Analyzing the options.
(A) 3-chloro-5-methyl cyclopentanol: Incorrect — The position of the chlorine and methyl groups is wrong.
(B) 1-chloro-3-methyl cyclopentan-4-ol: Incorrect — The positions of the chlorine and hydroxyl groups are incorrect.
(C) 4-chloro-2-methyl cyclopentan-ol: Correct — This is the correct IUPAC name based on the structure provided.
(D) 4-chloro-2-hydroxy-1-methylcyclopentane: Incorrect — The hydroxyl group is incorrectly named as hydroxy, and the methyl group is not on the correct position.
Step 3: Conclusion.
The correct answer is (C) 4-chloro-2-methyl cyclopentan-ol.