Match List I with List II and select the correct answer
`{:("List I",,"List II"),("(System)",,"(Expression for moment of inertia)"),("A. A ring about its axis",, (1) MR^(2)//2),("B. A uniform circular disc about its axis",,(2) 2//5MR^(2)),("C. A solid sphere about any diameter",,(3) 7//5MR^(2)),("D. A solid sphere about any tangent",,(4) MR^(2)):}`
Selec the answer from the codes given below

Options

A. `{:(A,,B,,C,,D),(2,,1,,3,,4):}`
B. `{:(A,,B,,C,,D),(4,,3,,2,,1):}`
C. `{:(A,,B,,C,,D),(1,,4,,3,,2):}`
D. `{:(A,,B,,C,,D),(4,,1,,2,,3):}`

Answer

To solve the problem of matching the systems in List I with their corresponding expressions for the moment of inertia in List II, we will go through each item step by step.

### Step-by-Step Solution:

1. **Identify the Moment of Inertia for a Ring about its Axis:**
- The moment of inertia \( I \) for a ring about its axis is given by the formula:
\[ I = MR^2 \]
- Therefore, for option A (A ring about its axis), the correct expression is:
- **A → (4) \( MR^2 \)**

2. **Identify the Moment of Inertia for a Uniform Circular Disc about its Axis:**
- The moment of inertia \( I \) for a uniform circular disc about its axis is given by the formula:
\[ I = \frac{1}{2} MR^2 \]
- Therefore, for option B (A uniform circular disc about its axis), the correct expression is:
- **B → (1) \( \frac{1}{2} MR^2 \)**

3. **Identify the Moment of Inertia for a Solid Sphere about any Diameter:**
- The moment of inertia \( I \) for a solid sphere about any diameter is given by the formula:
\[ I = \frac{2}{5} MR^2 \]
- Therefore, for option C (A solid sphere about any diameter), the correct expression is:
- **C → (2) \( \frac{2}{5} MR^2 \)**

4. **Identify the Moment of Inertia for a Solid Sphere about any Tangent:**
- The moment of inertia \( I \) for a solid sphere about a tangent is given by the formula:
\[ I = \frac{7}{5} MR^2 \]
- Therefore, for option D (A solid sphere about any tangent), the correct expression is:
- **D → (3) \( \frac{7}{5} MR^2 \)**

### Final Matching:
- A → (4) \( MR^2 \)
- B → (1) \( \frac{1}{2} MR^2 \)
- C → (2) \( \frac{2}{5} MR^2 \)
- D → (3) \( \frac{7}{5} MR^2 \)

### Conclusion:
The correct answer is:
- **4, 1, 2, 3**