The relative rate of esterification of compounds I, II, and III with p-nitrobenzoyl chloride depends on steric and electronic factors affecting the reaction at the hydroxyl group.

1. Structure Analysis:
   • I: The hydroxyl group is on a primary carbon, which usually has less steric hindrance, allowing for a faster esterification rate.
   • II: The hydroxyl group is on a secondary carbon. The increased steric hindrance compared to a primary carbon slows down the esterification rate.
   • III: The hydroxyl group is on a secondary carbon like II, but additional steric factors can further hinder the reaction.
2. Steric Hindrance and Reactivity:
   • Primary carbons (as in I) have less steric hindrance than secondary carbons, leading to faster reactions.
   • Among secondary carbons, further branching or substituents around the reactive site (as potentially seen in III) can decrease reactivity due to increased steric bulk.
3. Conclusion: Based on the steric effects and the structure of the compounds, the correct order of reactivity for esterification is I > II > III, as proposed by the correct answer.

Thus, the correct answer is I > II > III.