Logo
Jeeify
MCQMediumJEE 2025Dimensions & Dimensional Analysis

JEE Physics 2025 Question with Solution

Match List-I with List-II.

List-I

(A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility

List-II

(I) [ML−1T−1][ML^{-1}T^{-1}] (II) [ML−2T−3][ML^{-2}T^{-3}] (III) [ML−1T−2][ML^{-1}T^{-2}] (IV) [ML−1T−2][ML^{-1}T^{-2}]

  • A

    (A)–(I), (B)–(IV), (C)–(III), (D)–(I)

  • B

    (A)–(I), (B)–(III), (C)–(II), (D)–(I)

  • C

    (A)–(IV), (B)–(II), (C)–(III), (D)–(I)

  • D

    (A)–(IV), (B)–(I), (C)–(II), (D)–(III)

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Match the physical quantities in List-I with the dimensional formulas in List-II.

Find: The correct option.

The solution states that the correct option is B. The working shown there contains dimensional inconsistencies for intensity of wave, pressure gradient, and compressibility, so the listed derivation does not agree with the stated source answer. Since the extraction policy gives priority to the stated conclusion on the solution, the answer is recorded as B.

From the extracted the solution:

  • Coefficient of viscosity η\eta is matched with [ML−1T−1][ML^{-1}T^{-1}].
  • Intensity of wave is concluded there as power per unit area.
  • Pressure gradient is taken as pressure per unit distance.
  • Compressibility is taken as reciprocal of bulk modulus.

Therefore, as per the solution, the correct option is B.

Source Discrepancy Note

Given: the solution concludes with option B.

Find: Whether the shown dimensional working supports that conclusion.

The extracted working on the solution's states:

[η]=[ML−1T−1][\eta] = [ML^{-1}T^{-1}]

which is consistent for coefficient of viscosity.

For wave intensity, the page writes power per unit area, which gives:

[I]=[Power][Area]=[ML2T−3][L2]=[MT−3][I] = \frac{[\text{Power}]}{[\text{Area}]} = \frac{[ML^2T^{-3}]}{[L^2]} = [MT^{-3}]

This does not match any listed expression of the form [ML−2T−3][ML^{-2}T^{-3}] unless intensity is interpreted as energy flux per area with missing length dimensions already embedded in the listed option.

For pressure gradient, the page writes:

[Pressure gradient]=[Pressure][L]=[ML−1T−2][L]=[ML−2T−2][\text{Pressure gradient}] = \frac{[\text{Pressure}]}{[L]} = \frac{[ML^{-1}T^{-2}]}{[L]} = [ML^{-2}T^{-2}]

This again does not match the listed text in the question exactly.

For compressibility, the page writes reciprocal of pressure:

[K]=[M−1LT2][K] = [M^{-1}LT^2]

which also does not match the displayed List-II entries.

Hence, the solution's contains a mismatch between the displayed question data and the dimensional derivation. Nevertheless, the source explicitly declares The Correct Option is B, so the extracted answer is B.

Common mistakes

  • Confusing pressure with pressure gradient. Pressure has dimensions [ML−1T−2][ML^{-1}T^{-2}], but pressure gradient is pressure divided by distance, so one extra power of L−1L^{-1} must appear.

  • Treating compressibility as having the same dimensions as bulk modulus. Compressibility is the reciprocal of bulk modulus, so its dimensions are the inverse of pressure, not pressure itself.

  • Using energy per unit area instead of power per unit area incorrectly for wave intensity without checking the time factor. Intensity must include the correct time dependence.

Practice more Dimensions & Dimensional Analysis questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Dimensions & Dimensional Analysis

Related questions