(A) : Moment of inertia of a particle changes with axis of rotation.
(R ) : Moment of inertia depends on mass and distance of the particle from the axis of rotation.

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true but (R ) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze the assertion (A) and reason (R) given regarding the moment of inertia of a particle.

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
- The moment of inertia (I) of a particle about a given axis of rotation is defined as the product of the mass of the particle (m) and the square of its perpendicular distance (r) from the axis of rotation.
- Mathematically, it is expressed as:
\[ I = m \cdot r^2 \]

2. **Analyzing the Assertion (A)**:
- The assertion states that "the moment of inertia of a particle changes with the axis of rotation."
- This is true because the moment of inertia depends on the distance of the particle from the axis of rotation. If the axis of rotation changes, the distance (r) will also change, thus altering the moment of inertia.

3. **Analyzing the Reason (R)**:
- The reason states that "the moment of inertia depends on mass and distance of the particle from the axis of rotation."
- This is also true. The formula \( I = m \cdot r^2 \) shows that both mass and the distance from the axis of rotation are crucial factors in determining the moment of inertia.

4. **Conclusion**:
- Since both the assertion and the reason are true, and the reason correctly explains why the assertion is true, we conclude that both statements are correct.
- Therefore, the correct option is that both assertion and reason are correct, and the reason is the correct explanation for the assertion.

### Final Answer:
Both assertion (A) and reason (R) are correct, and the reason is the correct explanation for the assertion.

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