Match the column :
`{:(,"Column-I (Quantity)",,"Column-II(Unit)"),((a),"Energy density (Energy per unit volume)",(p),"dyne"//cm^(2)),((b),"Force constant of a spring",(r),kg-m//s),((c),"Pressure",(r),erg//cm^(2)),(,,(s),"pascal"):}`

Answer

To solve the problem of matching the quantities in Column-I with their respective units in Column-II, we will analyze each quantity step by step.

### Step 1: Analyze Energy Density
- **Quantity**: Energy density (Energy per unit volume)
- **Formula**: Energy density = Energy / Volume
- **Unit of Energy**: In SI, energy is measured in Joules (J), which is equivalent to kg·m²/s².
- **Unit of Volume**: Volume is measured in cubic meters (m³).
- **Unit of Energy Density**:
\[ \text{Energy Density} = \frac{\text{Energy}}{\text{Volume}} = \frac{\text{kg·m²/s²}}{\text{m³}} = \frac{\text{kg}}{\text{m·s²}} \]
- **Matching Unit**: The unit for energy density is not directly given in Column-II, but it can be compared to the options. The closest match in CGS would be erg/cm³, which is equivalent to dyne/cm².

### Step 2: Analyze Force Constant of a Spring
- **Quantity**: Force constant of a spring
- **Formula**: The force constant (k) is derived from Hooke's Law: F = -kx, where F is force and x is displacement.
- **Unit of Force**: In SI, force is measured in Newtons (N), which is kg·m/s².
- **Unit of k**:
\[ k = \frac{F}{x} = \frac{\text{N}}{\text{m}} = \frac{\text{kg·m/s²}}{\text{m}} = \frac{\text{kg}}{\text{s²}} \]
- **Matching Unit**: This matches with the unit given in Column-II as kg·m/s.

### Step 3: Analyze Pressure
- **Quantity**: Pressure
- **Definition**: Pressure is defined as force per unit area.
- **Unit of Pressure**: In SI, pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m².
- **Matching Unit**: The unit of pressure is directly given as Pascal (Pa) in Column-II.

### Summary of Matches
- **a)** Energy density matches with **(p)** dyne/cm² (as erg/cm³).
- **b)** Force constant of a spring matches with **(r)** kg·m/s.
- **c)** Pressure matches with **(s)** Pascal.

### Final Matches
- **(a)** → (p)
- **(b)** → (r)
- **(c)** → (s)