Match the following.
`|{:(,"Table-1",,"Table-2"),((A),"Coefficient of viscosity",(P),[M^(2)L^(-1)T^(-2)]),((B),"Surface tension",(Q),[ML^(0)T^(-2)]),((C),"Modulus of elasticity",(R),[ML^(-1) T^(-2)]),((D),"Energy per unit volume",(S),"None"),(,"of a fiuid",,):}|`

Answer

To solve the matching question, we need to determine the dimensional formulas for each of the properties listed in Table 1 and match them with the corresponding options in Table 2.

### Step-by-Step Solution:

1. **Coefficient of Viscosity (A)**:
- The coefficient of viscosity (η) is defined as the ratio of shear stress to shear rate.
- Its dimensional formula can be derived as follows:
- Shear stress = Force/Area = [M L T^(-2)] / [L^2] = [M L^(-1) T^(-2)]
- Shear rate = Velocity/Distance = [L T^(-1)] / [L] = [T^(-1)]
- Therefore, the dimensional formula of viscosity is:
\[ \text{Viscosity} = \frac{\text{Shear Stress}}{\text{Shear Rate}} = \frac{[M L^{-1} T^{-2}]}{[T^{-1}]} = [M L^{-1} T^{-1}] \]
- Since this option is not available in Table 2, we match A with S (None).

2. **Surface Tension (B)**:
- Surface tension (σ) is defined as force per unit length.
- Its dimensional formula is:
\[ \text{Surface Tension} = \frac{\text{Force}}{\text{Length}} = \frac{[M L T^{-2}]}{[L]} = [M L^{0} T^{-2}] \]
- Therefore, we match B with Q.

3. **Modulus of Elasticity (C)**:
- The modulus of elasticity (E) is defined as stress over strain.
- Its dimensional formula can be derived as follows:
- Stress = Force/Area = [M L T^(-2)] / [L^2] = [M L^(-1) T^(-2)]
- Strain is dimensionless.
- Therefore, the dimensional formula of modulus of elasticity is:
\[ \text{Modulus of Elasticity} = \frac{\text{Stress}}{\text{Strain}} = [M L^{-1} T^{-2}] \]
- Thus, we match C with R.

4. **Energy per Unit Volume (D)**:
- Energy per unit volume can be defined as energy divided by volume.
- Its dimensional formula is:
\[ \text{Energy} = [M L^2 T^{-2}], \quad \text{Volume} = [L^3] \]
- Therefore, energy per unit volume is:
\[ \text{Energy per Unit Volume} = \frac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}] \]
- Since this option is not available in Table 2, we match D with P.

### Final Matching:
- A → S (None)
- B → Q ([M L^{0} T^{-2}])
- C → R ([M L^{-1} T^{-2}])
- D → P ([M L^{-1} T^{-2}])