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Physics Question 27 – JEE-MAIN 2025

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Match List - I with List - II. List - IList - II(A) Coefficient of viscosity(I) [ML0T−3](B) Intensity of wave(II) [ML−2T−2](C) Pressure gradient(III) [M−1LT2](D) Compressibility(IV) [ML−1T−1] Choose the correct answer from the options given below :

Recall the fundamental dimensions of mass (M), length (L), and time (T) for all physical quantities.

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Ninja Strategy•Single Dimension Elimination

Calculate the dimension for 'Coefficient of viscosity' (A) first. Its dimension is [ML−1T−1], which corresponds to (IV). Only option 4 has (A)-(IV), thus eliminating all other options immediately.

● Video Walkthrough
Step 1: Determine dimensions for Coefficient of viscosity✦ Active

The coefficient of viscosity (η) is defined by Stokes' Law, F=6πηrv, where F is force, r is radius, and v is velocity.

η=F6πrv=[MLT−2][L][LT−1]=[ML−1T−1]

This matches (A) with (IV).

Step 2: Determine dimensions for Intensity of wave and Pressure gradient○ Expand

Intensity of wave (I) is defined as power per unit area. Pressure gradient is pressure per unit length.

I=PowerArea=[ML2T−3][L2]=[ML0T−3] Pressure gradient=PressureLength=[ML−1T−2][L]=[ML−2T−2]

This matches (B) with (I) and (C) with (II).

Step 3: Determine dimensions for Compressibility and Final Match○ Expand

Compressibility (κ) is the reciprocal of Bulk Modulus (B). Bulk Modulus has the same dimensions as pressure.

κ=1B=1Pressure=1[ML−1T−2]=[M−1L1T2]

This matches (D) with (III). Combining all matches, we get (A)-(IV), (B)-(I), (C)-(II), (D)-(III).

💡 Teacher's Secret Hint

Ensure to correctly invert the dimensions when taking the reciprocal of a quantity.

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