(A) : Moment of inertia plays the same role in rotational motion, as mass plays in linear motion.
(R ) : Moment of inertia depends only on mass of the body.

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 analyze the given statements regarding moment of inertia and its role in rotational motion, let's break down the assertion and reason step by step.

### Step 1: Understanding the Assertion
The assertion states that "Moment of inertia plays the same role in rotational motion as mass plays in linear motion."

- **Explanation**: In linear motion, mass is a measure of an object's resistance to acceleration when a force is applied (Newton's second law: F = ma). Similarly, in rotational motion, moment of inertia (I) measures an object's resistance to angular acceleration when a torque is applied (τ = Iα). Thus, the assertion is correct.

### Step 2: Understanding the Reason
The reason states that "Moment of inertia depends only on the mass of the body."

- **Explanation**: Moment of inertia (I) is calculated using the formula I = Σ(m_i * r_i²), where m_i is the mass of each particle and r_i is the distance from the axis of rotation. This shows that moment of inertia depends not only on the mass of the body but also on how far the mass is distributed from the axis of rotation. Therefore, the reason is incorrect.

### Conclusion
- The assertion is true: Moment of inertia does play a similar role in rotational motion as mass does in linear motion.
- The reason is false: Moment of inertia depends on both the mass of the body and its distribution relative to the axis of rotation.

### Final Answer
- Assertion (A) is true.
- Reason (R) is false.