Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below:

Explanation:
Let us derive the dimensional formula for each physical quantity step-by-step to find the correct match:

1. Angular Momentum (A):
The formula for angular momentum is \( L = mvr \), where \( m \) is mass, \( v \) is velocity, and \( r \) is radius.
Dimensions: \( [M] \times [LT^{-1}] \times [L] = [ML^2T^{-1}] \)
This matches with item (III).

2. Torque (B):
The formula for torque is \( \tau = \text{Force} \times \text{perpendicular distance} \).
Dimensions: \( [MLT^{-2}] \times [L] = [ML^2T^{-2}] \)
This matches with item (I).

3. Stress (C):
The formula for stress is \( \text{Stress} = \frac{\text{Force}}{\text{Area}} \).
Dimensions: \( \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}] \)
This matches with item (IV).

4. Pressure Gradient (D):
The formula for pressure gradient is \( \text{Pressure gradient} = \frac{\text{Pressure}}{\text{Distance}} \).
Dimensions: \( \frac{[ML^{-1}T^{-2}]}{[L]} = [ML^{-2}T^{-2}] \)
This matches with item (II).

Combining these results, the correct matching sequence is: (A) – (III), (B) – (I), (C) – (IV), (D) – (II).

Hence, Option B is the correct choice.