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MCQEasyJEE 2023Dimensions & Dimensional Analysis

JEE Physics 2023 Question with Solution

Match List I with List II.

Two-column matching table with List I: A Torque, B Energy density, C Pressure gradient, D Impulse; and List II: I $$kg\, m^{-1} s^{-2}$$, II $$kg\, m s^{-1}$$, III $$kg\, m^{-2} s^{-2}$$, IV $$kg\, m^{2} s^{-2}$$.

Choose the correct answer from the options given below:

  • A

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

  • B

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

  • C

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

  • D

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

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A matching question on dimensions/units of torque, energy density, pressure gradient, and impulse.

Find: The correct matching between List I and List II.

From the solution:

  • A: Torque ⇒\Rightarrow IV : kg m2s−2kg\, m^{2} s^{-2}
  • B: Energy density ⇒\Rightarrow I : kg m−1s−2kg\, m^{-1} s^{-2}
  • C: Pressure gradient ⇒\Rightarrow III : kg m−2s−2kg\, m^{-2} s^{-2}
  • D: Impulse ⇒\Rightarrow II : kg ms−1kg\, m s^{-1}

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

The correct option is A.

Common mistakes

  • Confusing energy density with pressure gradient. Energy density has the same unit as pressure, kg m−1s−2kg\, m^{-1} s^{-2}, whereas pressure gradient introduces one more factor of m−1m^{-1}. Check whether the quantity is a value or a rate of change with position.

  • Using the unit of force for impulse. Impulse is force multiplied by time, so its unit is kg ms−1kg\, m s^{-1}, not kg ms−2kg\, m s^{-2}. Always include the extra factor of time.

  • Mistaking torque for force. Torque equals force multiplied by perpendicular distance, so its unit is kg m2s−2kg\, m^{2} s^{-2}. Multiply the force unit by length before matching.

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