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MCQEasyJEE 2023Dimensions & Dimensional Analysis

JEE Physics 2023 Question with Solution

Match List-I with List-II.

List-I List-II A. Angular momentum I. [ML2T−2][ML^2T^{-2}] B. Torque II. [ML2T−2][ML^2T^{-2}] C. Stress III. [ML−2T−2][ML^{-2}T^{-2}] D. Pressure gradient IV. [ML−1T−2][ML^{-1}T^{-2}] Choose the correct answer from the options given below:

  • A

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

  • B

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

  • C

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

  • D

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

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: A matching question on dimensional formulas of angular momentum, torque, stress, and pressure gradient.

Find: The correct correspondence between List-I and List-II.

We match each physical quantity with its dimensional formula:

  • Angular momentum (A): The dimensional formula is [ML2T−1][ML^2T^{-1}], so it matches III.
  • Torque (B): The dimensional formula is [ML2T−2][ML^2T^{-2}], so it matches I.
  • Stress (C): Stress is force per unit area, so its dimensional formula is [ML−1T−2][ML^{-1}T^{-2}], so it matches IV.
  • Pressure gradient (D): Pressure gradient is pressure per unit length, so its dimensional formula is [ML−2T−2][ML^{-2}T^{-2}], so it matches II.

Thus, the correct matching is A-III, B-I, C-IV, D-II. Therefore, the correct option is B.

Common mistakes

  • Confusing angular momentum with torque because both involve rotational motion. This is incorrect because angular momentum has dimension [ML2T−1][ML^2T^{-1}] whereas torque has dimension [ML2T−2][ML^2T^{-2}]. Always write the defining formula before matching.

  • Treating stress and pressure gradient as the same quantity. This is wrong because stress has the same dimensions as pressure, [ML−1T−2][ML^{-1}T^{-2}], while pressure gradient is pressure divided by length, giving [ML−2T−2][ML^{-2}T^{-2}]. Divide by an additional length for gradient.

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