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MCQEasyJEE 2023Dimensions & Dimensional Analysis

JEE Physics 2023 Question with Solution

Match List – I with List – II

A matching question image showing List I and List II entries for physical quantities and their dimensional formulas to be matched.

Choose the correct answer from the options given below:

  • A

    A – II, B – IV, C – I, D – III

  • B

    A – I, B – III, C – IV, D – II

  • C

    A – IV, B – III, C – II, D – I

  • D

    A – IV, B – II, C – I, D – III

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A matching question between physical quantities and their dimensional formulas.

Find: The correct correspondence between A, B, C, D and I, II, III, IV.

From the solution:

  • A: Torque ⇒\Rightarrow IV : kg m2 s−2\mathrm{kg\, m^2\, s^{-2}}
  • B: Energy density ⇒\Rightarrow I : kg m−1 s−2\mathrm{kg\, m^{-1}\, s^{-2}}
  • C: Pressure gradient ⇒\Rightarrow III : kg m−2 s−2\mathrm{kg\, m^{-2}\, s^{-2}}
  • D: Impulse ⇒\Rightarrow II : kg m s−1\mathrm{kg\, m\, s^{-1}}

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

The solution explicitly states: The Correct Option is A.

So, the correct option is A.

Note: This disagrees with the answer key, but the solution is taken.

Common mistakes

  • Matching torque with the dimensions of force. This is wrong because torque equals force multiplied by distance, so one extra power of length appears. Use [τ]=[F][r]=kg m2 s−2[\tau] = [F][r] = \mathrm{kg\, m^2\, s^{-2}}.

  • Confusing energy density with pressure only by name without checking dimensions carefully. Although they have the same dimensions, the match must follow the listed formulas exactly. Verify using energy per unit volume.

  • Treating pressure gradient as pressure itself. This is wrong because gradient means pressure per unit length, introducing one more factor of m−1m^{-1}. So divide the dimensions of pressure by length.

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