Match List-I with List-II.
$$\begin{array}{|l|l|l|l|}\hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Power per unit area} & \text{I.} & [\text{ML}^{-1}\text{T}^{-2}] \\ \hline \text{B.} & \text{Impulse per unit mass per unit time} & \text{II.} & [\text{L}^2\text{T}^{-1}] \\ \hline \text{C.} & \text{Angular momentum per unit mass} & \text{III.} & [\text{MT}^{-3}] \\ \hline \text{D.} & \text{Work done per unit volume} & \text{IV.} & [\text{LT}^{-2}] \\ \hline \end{array}$$
Choose the correct answer from the options given below:
Answer: (C) A-III, B-IV, C-II, D-I
Concept. Build each quantity from its definition and divide out the stated per-unit quantities.
Step 1. Power per unit area.
$$\frac{[\text{ML}^2\text{T}^{-3}]}{[\text{L}^2]} = [\text{MT}^{-3}] \;\to\; \text{III}$$
Step 2. Impulse per unit mass per unit time. Impulse per unit mass is a velocity; per unit time it is an acceleration:
$$\frac{[\text{MLT}^{-1}]}{[\text{M}][\text{T}]} = [\text{LT}^{-2}] \;\to\; \text{IV}$$
Step 3. Angular momentum per unit mass.
$$\frac{[\text{ML}^2\text{T}^{-1}]}{[\text{M}]} = [\text{L}^2\text{T}^{-1}] \;\to\; \text{II}$$
Step 4. Work per unit volume.
$$\frac{[\text{ML}^2\text{T}^{-2}]}{[\text{L}^3]} = [\text{ML}^{-1}\text{T}^{-2}] \;\to\; \text{I}$$
Answer. A-III, B-IV, C-II, D-I (Option C).
Solution by Sreeraj P, M.Sc Physics