A : In purc rolling motion all the points of a rigid body have same linear velocity.
R : Rolling motion is not possible on smooth surface.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion,
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion,
C. If Assertion is true statement but Reason is false,
D. If both Assertion and Reason are false statements,

Answer

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

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states, "In pure rolling motion, all points of a rigid body have the same linear velocity."
- In pure rolling motion, a rigid body (like a wheel) rolls without slipping. This means that the point of contact with the ground is momentarily at rest while the rest of the body moves.
- The topmost point of the rolling body has a linear velocity that is the sum of the translational velocity (V) and the rotational velocity (ωr), while the bottommost point has a linear velocity that is the difference of the translational velocity and the rotational velocity (V - ωr).
- Therefore, the assertion is **false** because not all points have the same linear velocity.

2. **Understanding the Reason (R)**:
- The reason states, "Rolling motion is not possible on a smooth surface."
- In reality, rolling motion can occur on a smooth surface, but it requires friction to prevent slipping. A perfectly smooth surface would not provide the necessary friction for pure rolling motion.
- Thus, the reason is also **false** because rolling motion can occur on smooth surfaces if there is sufficient friction.

3. **Conclusion**:
- Since both the assertion and the reason are false, the correct answer is that both statements are false.

### Final Answer:
Both assertion and reason are false.