Match List-I with List-II: Choose the correct answer from the opt… — Solution | JEE Physics

MCQMediumJEE 2023Dimensions & Dimensional Analysis

Match List-I with List-II: Choose the correct answer from the options given below:

Answer

Correct answer:A

Standard Method

Given: A match-the-list question on dimensional formulas.

Find: The correct correspondence between the quantities in List-I and the dimensional formulas in List-II.

From the solution:

\frac{\Delta P}{\Delta x} = \frac{[M^1L^{-1}T^{-2}]}{[L]} = [M^1L^{-2}T^{-2}]

\frac{\text{Energy}}{\text{Volume}} = \frac{[M^1L^2T^{-2}]}{[L^3]} = [M^1L^{-1}T^{-2}]

\frac{\text{Force}}{\text{Charge}} = \frac{[M^1L^1T^{-2}]}{[A^1T^1]} = [M^1L^1T^{-3}A^{-1}]

\frac{\text{Heat energy}}{\text{Mass}} = \frac{[M^1L^2T^{-2}]}{[M]} = [M^0L^2T^{-2}]

These derived dimensional formulas match the sequence given in option A.

Therefore, the correct option is A.

Students often use the dimensional formula of pressure directly for pressure gradient. This is wrong because a gradient means division by length. Always divide the dimension of pressure by $[L]$ .
A common mistake is to confuse energy density with pressure numerically and then stop without checking dimensions carefully. Even if they share the same dimensions in some contexts, the matching must still be done by proper derivation from definition.
Many students write charge as a separate base quantity instead of converting it to $[AT]$ . This gives the wrong dimension for electric field. Always use $\text{Charge} = [A^1T^1]$ in SI base dimensions.

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