With regard to dependence of quantities given in column I and II, match the following.
`{:(,"Column I",,"Column II"),((A),"Young's modulus of a substance ",(p),"Depends on temperature"),((B),"Bulk modulus of a substance",(q),"Depends on length"),((C),"Modulus of rigidity of a substance",(r),"Depends on area of cross-section"),((D),"Volume of a substance",(s),"Depends on the nature of material"):}`

Options

A. `{:(A,B,C,D),("p,s","q,s","p,s","p,q"):}`
B. `{:(A,B,C,D),("p,s","p,s","p,s","p,q"):}`
C. `{:(A,B,C,D),("p,s","p,s","p,s","p,q,r"):}`
D. `{:(A,B,C,D),("p,q,r","p,s","p,s","p,r"):}`

Explanation

To solve the matching question regarding the dependence of quantities in Column I and Column II, we will analyze each item in Column I and determine its corresponding match in Column II based on the properties of elasticity and volume.

### Step-by-Step Solution:

1. **Young's Modulus of a Substance (A)**:
- Young's modulus measures the tensile elasticity of a material. It is defined as the ratio of tensile stress to tensile strain.
- Young's modulus depends on the nature of the material and is independent of its dimensions (length and area).
- **Match**: (A) → (s) "Depends on the nature of material".

2. **Bulk Modulus of a Substance (B)**:
- Bulk modulus measures a substance's resistance to uniform compression. It is defined as the ratio of volumetric stress to the change in volume strain.
- Like Young's modulus, bulk modulus also depends on the nature of the material and is independent of its dimensions.
- **Match**: (B) → (s) "Depends on the nature of material".

3. **Modulus of Rigidity of a Substance (C)**:
- Modulus of rigidity (or shear modulus) measures a material's response to shear stress. It is defined as the ratio of shear stress to shear strain.
- This modulus also depends on the nature of the material and is independent of its dimensions.
- **Match**: (C) → (s) "Depends on the nature of material".

4. **Volume of a Substance (D)**:
- The volume of a substance is determined by its dimensions, specifically its length and area (Volume = Area × Length).
- Additionally, the volume can change with temperature due to thermal expansion.
- **Match**: (D) → (p) "Depends on temperature" and (q) "Depends on length" and (r) "Depends on area of cross-section".

### Final Matching:
- A → s (Depends on the nature of material)
- B → s (Depends on the nature of material)
- C → s (Depends on the nature of material)
- D → p (Depends on temperature), q (Depends on length), r (Depends on area of cross-section)

### Summary of Matches:
- (A) Young's modulus of a substance → (s)
- (B) Bulk modulus of a substance → (s)
- (C) Modulus of rigidity of a substance → (s)
- (D) Volume of a substance → (p), (q), (r)