Step 1: Analyze the functional groups

To determine polarity, we examine the dipole moment and intermolecular forces of each compound:

• A: Diethyl ether ($CH_{3}CH_{2}OCH_{2}CH_{3}$) - Weakly polar due to C-O-C bond.
• B: Ethanol ($CH_{3}CH_{2}OH$) - Polar due to -OH group, capable of hydrogen bonding.
• C: Acetone ($CH_{3}COCH_{3}$) - Polar due to C=O bond, but lacks hydrogen bonding.
• D: Acetic acid ($CH_{3}COOH$) - Highly polar due to the presence of both C=O and -OH groups, allowing for strong hydrogen bonding and resonance.

Step 2: Compare dipole moments and intermolecular interactions

The polarity order is governed by the strength of the dipole and the ability to form hydrogen bonds:

• Diethyl ether (A) has the lowest polarity among the four.
• Acetone (C) has a higher dipole moment than ether due to the strong C=O bond.
• Ethanol (B) has a significant dipole and can form intermolecular hydrogen bonds, making it more polar than acetone.
• Acetic acid (D) is the most polar because the carboxyl group (-COOH) exhibits strong polarity and extensive hydrogen bonding.

Step 3: Arrange in increasing order

Based on the analysis: $$A < C < B < D$$