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MCQEasyJEE 2024Dimensions & Dimensional Analysis

JEE Physics 2024 Question with Solution

Match List-I with List-II. List-I | List-II A. Coefficient of viscosity | I. [ML−1T−1][ML^{-1}T^{-1}] B. Surface Tension | II. [ML0T−2][ML^{0}T^{-2}] C. Angular momentum | III. [ML2T−1][ML^{2}T^{-1}] D. Rotational kinetic energy | IV. [ML2T−2][ML^{2}T^{-2}]

  • A

    A-I, B-II, C-III, D-IV

  • B

    A-I, B-II, C-IV, D-III

  • C

    A-III, B-IV, C-II, D-I

  • D

    A-IV, B-III, C-II, D-I

Answer

Correct answer:C

Step-by-step solution

Standard Method

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

Find: The correct matching.

Use dimensional analysis for each quantity:

  1. Coefficient of viscosity
η=FA⋅dydv/dt\eta = \frac{F}{A} \cdot \frac{dy}{dv/dt}

Hence,

[η]=[ML−1T−1][\eta] = [ML^{-1}T^{-1}]
  1. Surface tension
S.T=FLS.T = \frac{F}{L}

Hence,

[S.T]=[ML0T−2][S.T] = [ML^{0}T^{-2}]
  1. Angular momentum
L=mvrL = mvr

Hence,

[L]=[ML2T−1][L] = [ML^{2}T^{-1}]
  1. Rotational kinetic energy
K.E.=12Iω2K.E. = \frac{1}{2} I\omega^2

Hence,

[K.E.]=[ML2T−2][K.E.] = [ML^{2}T^{-2}]

Therefore the matching is:

  • A →\rightarrow III
  • B →\rightarrow IV
  • C →\rightarrow II
  • D →\rightarrow I

So, the correct option is C.

Step-by-step Dimensional Matching

Given: The quantities are coefficient of viscosity, surface tension, angular momentum, and rotational kinetic energy.

Find: Which option gives the correct dimensional correspondence.

From the extracted solution:

  • Coefficient of viscosity has dimension [ML−1T−1][ML^{-1}T^{-1}].
  • Surface tension has dimension [ML0T−2][ML^{0}T^{-2}].
  • Angular momentum has dimension [ML2T−1][ML^{2}T^{-1}].
  • Rotational kinetic energy has dimension [ML2T−2][ML^{2}T^{-2}].

Comparing with the labels in List-II as presented in the source solution, the conclusion written there is: A-III, B-IV, C-II, D-I.

Hence, the correct option marked on the solution is C.

Common mistakes

  • Confusing surface tension with energy per unit area without checking the dimensional form. Here the required relation is force per unit length, so use FL\frac{F}{L} to identify the correct dimension.

  • Mixing up angular momentum and rotational kinetic energy. Angular momentum has one power of time in the denominator, [ML2T−1][ML^{2}T^{-1}], whereas energy has [ML2T−2][ML^{2}T^{-2}].

  • Matching directly by option pattern without evaluating each quantity. Always write the dimensional formula of each physical quantity first, then compare with the listed symbols.

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