Question

Match List I with List II:

List-I (Physical Quantity)		List-II (Dimensional Formula)
(A)	Pressure Gradient	(I)	\([M^0L^2T^{–2}]\)
(B)	Energy density	(II)	\([M^1L^{–1}T^{–2}]\)
(C)	Electric field	(III)	\([M^1L^{–2}T^{–2}]\)
(D)	Latent heat	(IV)	\([M^1L^1T^{–3}A^{–1}]\)

Choose the correct answer from the options given below:

• A. A-III, B-II, C-IV, D-I
• B. A-II, B-III, C-l, D-IV
• C. A-III, B-II, C-I, D-IV
• D. A-II, B-III, C-IV, D-I

Hint:

For matching dimensional formulas:
• Analyze the definition or physical meaning of the quantity.
• Break it into base quantities and derive the dimensional formula.

Answer 1

The Correct Option is A

• Pressure gradient: \[ \frac{\Delta P}{\Delta x} = \frac{[M^1L^{-1}T^{-2}]}{[L]} = [M^1L^{-2}T^{-2}]. \]
• Energy density: \[ \frac{\text{Energy}}{\text{Volume}} = \frac{[M^1L^2T^{-2}]}{[L^3]} = [M^1L^{-1}T^{-2}]. \]
• Electric field: \[ \frac{\text{Force}}{\text{Charge}} = \frac{[M^1L^1T^{-2}]}{[A^1T^1]} = [M^1L^1T^{-3}A^{-1}]. \]
• Latent heat: \[ \frac{\text{Heat energy}}{\text{Mass}} = \frac{[M^1L^2T^{-2}]}{[M]} = [M^0L^2T^{-2}]. \]