Match List I with List II: Choose the correct answer from the options given below: List I (Physical Quantity) List II (Dimensional Formula) A. Pressure gradient I. [M⁰L²T⁻²] B. Energy density II. [M¹L⁻¹T⁻²] C. Electric Field III. [M¹L⁻²T⁻²] D. Latent heat IV. [M¹L¹T⁻³A⁻¹] (a) A-III, B-II, C-IV, D-I (b) A-III, B-II, C-I, D-IV (c) A-II, B-III, C-IV, D-I (d) A-II, B-III, C-I, D-IV

Answer: (a). Pressure gradient = P/L = ML⁻²T⁻² (A-III). Energy density = energy/volume = ML⁻¹T⁻² (B-II). Electric field = F/q = MLT⁻³A⁻¹ (C-IV). Latent heat = energy/mass = L²T⁻² (D-I). So the answer is (a) A-III, B-II, C-IV, D-I.

Match List I with List II: Choose the correct answer from the options… | JEE Main 2023 (29 Jan, Shift 1)

Q31JEE Main 2023 · 29 JAN · SHIFT 1Medium

Applications of Dimensional Analysis

Match List I with List II:

Choose the correct answer from the options given below:

	List I (Physical Quantity)		List II (Dimensional Formula)
A.	Pressure gradient	I.	$\left[\mathrm{M^{0}L^{2}T^{-2}}\right]$
B.	Energy density	II.	$\left[\mathrm{M^{1}L^{-1}T^{-2}}\right]$
C.	Electric Field	III.	$\left[\mathrm{M^{1}L^{-2}T^{-2}}\right]$
D.	Latent heat	IV.	$\left[\mathrm{M^{1}L^{1}T^{-3}A^{-1}}\right]$

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Answer: (a)

Pressure gradient $= P/L = ML^{-2}T^{-2}$ (A-III).
Energy density $=$ energy/volume $= ML^{-1}T^{-2}$ (B-II).
Electric field $= F/q = MLT^{-3}A^{-1}$ (C-IV).
Latent heat $=$ energy/mass $= L^2T^{-2}$ (D-I).
So the answer is (a) A-III, B-II, C-IV, D-I.

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