Compounds A and B, having the same molecular formula \( C_4H_8O \), react separately with \( CH_3MgBr \), followed by reaction with dil. HCl to form compounds X and Y respectively. Compound Y undergoes acidic dehydration in the presence of Conc. \( H_2SO_4 \) much more readily than X. Compound Y also reacts with Lucas reagent, much more readily than X, with the appearance of turbidity. Identify X and Y.
Given that compounds A and B have the same molecular formula, both will likely be alcohols that react with CH\(_3\)MgBr to form alkylated products. Since compound Y undergoes acidic dehydration more readily, this suggests it has a structure that allows for easier elimination of water. When reacting with Lucas reagent, compound Y also reacts more readily, indicating it is a more reactive alcohol.
The Lucas test typically distinguishes between primary, secondary, and tertiary alcohols, with tertiary alcohols reacting most rapidly. Thus, Y must be a more substituted alcohol, which fits the structure of 2-Methylbutan-2-ol, a secondary alcohol. On the other hand, X is a primary alcohol, pentan-2-ol, which reacts less readily under the same conditions.
Thus, the correct identification for X is Pentan-2-ol and for Y is 2-Methylbutan-2-ol.
If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are $ a $, $ b $, and $ c $ respectively, then the corresponding ratio of increase in their lengths would be: