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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. $$[M^1L^1T^{-3}A^{-1}]$$ |
We need to find the dimensional formula for each physical quantity and match with the given list.
A. Pressure gradient:
Pressure gradient = $$\frac{\text{Pressure}}{\text{Distance}}$$
Dimension of Pressure = $$[M^1L^{-1}T^{-2}]$$
Dimension of Pressure gradient = $$\frac{[M^1L^{-1}T^{-2}]}{[L]} = [M^1L^{-2}T^{-2}]$$
This matches with III.
B. Energy density:
Energy density = $$\frac{\text{Energy}}{\text{Volume}}$$
Dimension of Energy = $$[M^1L^2T^{-2}]$$
Dimension of Energy density = $$\frac{[M^1L^2T^{-2}]}{[L^3]} = [M^1L^{-1}T^{-2}]$$
This matches with II.
C. Electric Field:
Electric Field = $$\frac{\text{Force}}{\text{Charge}}$$
Dimension of Force = $$[M^1L^1T^{-2}]$$
Dimension of Charge = $$[A^1T^1]$$
Dimension of Electric Field = $$\frac{[M^1L^1T^{-2}]}{[A^1T^1]} = [M^1L^1T^{-3}A^{-1}]$$
This matches with IV.
D. Latent heat:
Latent heat = $$\frac{\text{Heat Energy}}{\text{Mass}}$$
Dimension of Latent heat = $$\frac{[M^1L^2T^{-2}]}{[M^1]} = [M^0L^2T^{-2}]$$
This matches with I.
Therefore: A-III, B-II, C-IV, D-I
The correct answer is Option 3.
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