C

Step 1: Understanding the physical quantities and their dimensional formulas
1. **Coefficient of viscosity:** The coefficient of viscosity ($\mu$) describes a fluid's internal resistance to flow. Its units can be derived from the formula:
$$ \text{Dimensions} = \text{Force} \times \text{Time} / \text{Area} \Rightarrow [ML^–1T^–1] $$
2. **Surface tension:** It describes the force per unit length acting on the surface of a liquid. It is defined as:
$$ \gamma = \frac{F}{L} \Rightarrow [ML^0T^–2] $$
3. **Modulus of elasticity:** This measures a material's tendency to deform when under tension or compression. It is derived from:
$$ E = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L} \Rightarrow [ML^–1T^–2] $$
4. **Energy per unit volume of a fluid:** Energy density, which can be written as:
$$ \text{Energy} = \frac{Work}{Volume} \Rightarrow [ML^–2T^–2] $$
Step 2: Matching the correct options
Based on the dimensional analyses:
(i) Coefficient of viscosity → [C] [ML^–1T^–1]
(ii) Surface tension → [B] [ML^0T^–2]
(iii) Modulus of elasticity → [A] [ML^–1T^–2]
(iv) Energy per unit volume of a fluid → [D] None.
Thus, matching yields:
- (i): [C]
- (ii): [B]
- (iii): [A]
- (iv): [D]
Therefore, the correct answer option is C.