Match List I with List II: Answer: (1) (A) – III, (B) – I, (C) – II, (D) – IV

Given: A matching question on dimensional formulas. Find: The correct option that matches each quantity with its dimensional formula. Use the physical definition of each quantity and write its dimensional formula. For pressure gradient: P x = [M^1L^-1T^-2][L] = [M^1L^-2T^-2] For energy density: Energy Volume = [M^1L^2T^-2][L^3] = [M^1L^-1T^-2] For electric field: Force Charge = [M^1L^1T^-2][A^1T^1] = [M^1L^1T^-3A^-1] For latent heat: Heat energy Mass = [M^1L^2T^-2][M] = [M^0L^2T^-2] Comparing these with the given lists, the correct matching is (A) – III, (B) – I, (C) – II, (D) – IV. Therefore, the correct option is A.

Match List I with List II: Answer: (1) (A) – III, (B) – I, (C) –… — Solution | JEE Physics

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Match List I with List II:

Answer: $\text{(1) (A) – III, (B) – I, (C) – II, (D) – IV}$

A
$\text{(A) – III, (B) – I, (C) – II, (D) – IV}$
B
$\text{(A) – I, (B) – II, (C) – IV, (D) – III}$
C
$\text{(A) – II, (B) – I, (C) – IV, (D) – III}$
D
$\text{(A) – III, (B) – I, (C) – IV, (D) – II}$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A matching question on dimensional formulas.

Find: The correct option that matches each quantity with its dimensional formula.

Use the physical definition of each quantity and write its dimensional formula.

For pressure gradient:

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

For energy density:

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

For electric field:

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

For latent heat:

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

Comparing these with the given lists, the correct matching is (A) – III, (B) – I, (C) – II, (D) – IV.

Therefore, the correct option is A.

Common mistakes

Confusing pressure with pressure gradient. Pressure has dimensions $[M^1L^{-1}T^{-2}]$ , but pressure gradient is pressure divided by length, so one extra $L^{-1}$ must appear. Always divide by the spatial coordinate explicitly.
Using energy density as energy per area instead of energy per volume. The correct expression is energy divided by volume, so divide by $[L^3]$ , not $[L^2]$ .
Writing electric field dimensions incorrectly by forgetting that charge has dimensions $[AT]$ . Since $E = \frac{F}{q}$ , divide force by $[A^1T^1]$ to get $[M^1L^1T^{-3}A^{-1}]$ .

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