Assertion : A solid sphere cannot roll without slipping on smooth horizontal surface
Reason : If the sphere is left free on smooth inclined surface. It cannot roll without slipping.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is fasle
D. If Assertion is false but Reason is true

Explanation

To analyze the assertion and reason provided in the question, we will break down the concepts involved in rolling motion and the conditions under which a solid sphere can roll without slipping.

### Step-by-Step Solution

1. **Understanding the Assertion**:
The assertion states that a solid sphere cannot roll without slipping on a smooth horizontal surface. To evaluate this, we need to consider the forces acting on the sphere when it is rolling.

- On a smooth horizontal surface, the only forces acting on the sphere are its weight (downward) and the normal force (upward). There are no horizontal forces acting on the sphere.
- Since there is no net horizontal force, the sphere can maintain a constant linear velocity. This means that it can roll without slipping if it has an initial velocity.

**Conclusion**: The assertion is **false** because a solid sphere can roll without slipping on a smooth horizontal surface if it is given an initial velocity.

2. **Understanding the Reason**:
The reason states that if the sphere is left free on a smooth inclined surface, it cannot roll without slipping. We will analyze this scenario.

- When the sphere is placed on a smooth inclined surface, the gravitational force acting on it can be resolved into two components: one parallel to the incline (mg sin θ) and one perpendicular to the incline (mg cos θ).
- Since the surface is smooth, there is no frictional force to provide the necessary torque for rolling. The only motion that occurs is translational due to the component of gravitational force acting down the incline.
- As a result, the sphere will slide down the incline without rolling, meaning it cannot roll without slipping.

**Conclusion**: The reason is **true** because the sphere will slide down the incline without rolling due to the lack of friction.

### Final Evaluation
- **Assertion**: False (A solid sphere can roll without slipping on a smooth horizontal surface).
- **Reason**: True (A solid sphere cannot roll without slipping on a smooth inclined surface).