Assertion (A) Two circular discs of equal mass and thickness made of different materials, will have same moment of inertia about their central axes of rotation.
Reason (R) Moment of inertia depends upon the distribution of mass in the body.

Options

A. Both A and R are correct and R is the correct explanation of A
B. Both A and R are correct but R is not correct explanation of A
C. A is correct but R is incorrect
D. A is incorrect but R is correct

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that two circular discs of equal mass and thickness made of different materials will have the same moment of inertia about their central axes of rotation.

2. **Understanding the Moment of Inertia**:
- The moment of inertia (I) of a disc about its central axis is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
- Here, \(m\) is the mass of the disc and \(r\) is the radius.

3. **Given Conditions**:
- Both discs have equal mass (let's denote this mass as \(m\)).
- Both discs have the same thickness (let's denote this thickness as \(T\)).
- The discs are made of different materials, which implies they have different densities.

4. **Calculating Volume and Radius**:
- The volume \(V\) of a disc can be expressed as:
\[ V = \text{Area} \times \text{Thickness} = \pi r^2 T \]
- Since mass \(m\) is related to density (\(\rho\)) and volume, we have:
\[ m = \rho V = \rho (\pi r^2 T) \]
- For two discs made of different materials, we can write:
\[ m_1 = \rho_1 (\pi r_1^2 T) \quad \text{and} \quad m_2 = \rho_2 (\pi r_2^2 T) \]
- Since \(m_1 = m_2\), we have:
\[ \rho_1 (\pi r_1^2 T) = \rho_2 (\pi r_2^2 T) \]
- Simplifying gives:
\[ \rho_1 r_1^2 = \rho_2 r_2^2 \]

5. **Moment of Inertia Calculation**:
- The moment of inertia for each disc can be calculated as:
\[ I_1 = \frac{1}{2} m r_1^2 \quad \text{and} \quad I_2 = \frac{1}{2} m r_2^2 \]
- Since \(m\) is the same for both discs, the moment of inertia will depend on \(r_1\) and \(r_2\):
\[ I_1 \neq I_2 \quad \text{(because \(r_1\) and \(r_2\) are different)} \]

6. **Conclusion for Assertion**:
- Since \(I_1\) and \(I_2\) are not equal, the assertion (A) is **incorrect**.

7. **Understanding the Reason (R)**:
- The reason states that the moment of inertia depends upon the distribution of mass in the body.
- This statement is **correct** because the moment of inertia is indeed influenced by how mass is distributed relative to the axis of rotation.

8. **Final Conclusion**:
- The assertion is incorrect, while the reason is correct. Therefore, the correct answer is that Assertion (A) is false and Reason (R) is true.