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Question 1

Match List I with List II:

List-I (Physical Quantity)List-II (Dimensional Formula)
A. Pressure gradientI. $$[M^0L^2T^{-2}]$$
B. Energy densityII. $$[M^1L^{-1}T^{-2}]$$
C. Electric FieldIII. $$[M^1L^{-2}T^{-2}]$$
D. Latent heatIV. $$[M^1L^1T^{-3}A^{-1}]$$

Choose the correct answer from the options given below:

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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