Step 1: Understanding the Concept:
Acidic \(KMnO_4\) is a strong oxidising agent. It breaks the \(C=C\) double bond of an alkene completely (oxidative cleavage). Each carbon of the double bond ends up as a carboxylic acid, or as a ketone if that carbon carries two alkyl groups.
Step 2: Structure of but-2-ene:
\(CH_3-CH=CH-CH_3\). Each double bond carbon carries one hydrogen and one methyl group.
Step 3: Cleavage:
Breaking the double bond gives two \(CH_3-CH\) fragments. Each is oxidised to \(CH_3COOH\).
\[ CH_3CH=CHCH_3 \xrightarrow{KMnO_4/H^+} 2\,CH_3COOH \]
Step 4: Why the other options are wrong:
Butanoic acid and butanol would keep all four carbons, but the chain is cut in the middle. Butanal is an aldehyde, which would be oxidised further under these conditions. So only acetic acid, option (B), is formed.
Final Answer:
But-2-ene is cleaved into two molecules of acetic acid.
\[ \boxed{B:\ \text{Acetic acid}} \]