The reaction given is:
\[ CH_3Br + Nu^- \rightarrow CH_3Nu + Br^- \]
This is a typical SN2 reaction because CH₃Br is a methyl halide. In SN2 reactions, the rate depends directly on the strength of the nucleophile.
Rate ∝ Nucleophilicity
All the species given are negatively charged nucleophiles. In such cases, nucleophilicity generally parallels basicity when steric hindrance is minimal.
Compare their basic strengths:
\[ OH^- \; \text{(strong base)} \]
\[ PhO^- \; \text{(phenoxide; resonance stabilized, less basic than OH^-)} \]
\[ CH_3COO^- \; \text{(acetate; strongly resonance stabilized, weaker base)} \]
\[ ClO_4^- \; \text{(perchlorate; highly resonance stabilized, very weak base)} \]
Greater resonance stabilization reduces electron density available for attack, thereby reducing nucleophilicity.
Thus, the decreasing order of nucleophilicity is:
\[ OH^- > PhO^- > CH_3COO^- > ClO_4^- \]
Hence, the rate of reaction follows the same order.
Correct Option: B