A : rigid body can't be in a pure rolling on a rough inclined plane without giving any external force.
R : Since there is no torque providing force acting on the body in the above case, the body can't come in a rolling condition.

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 problem, we need to analyze both the assertion (A) and the reason (R) provided in the question.

### Step 1: Understand the Assertion (A)
The assertion states that a rigid body cannot be in pure rolling on a rough inclined plane without giving any external force.

**Analysis:**
- A rigid body can roll down an inclined plane due to the gravitational force acting on it.
- The frictional force at the contact point between the rigid body and the inclined plane is crucial for rolling motion.
- Therefore, the assertion is incorrect because the body can roll due to the forces acting on it, including gravity and friction.

### Step 2: Understand the Reason (R)
The reason states that since there is no torque providing force acting on the body in the above case, the body can't come in a rolling condition.

**Analysis:**
- Torque is necessary for rolling motion, and it can be provided by the frictional force acting at the point of contact.
- The weight of the body also contributes to the torque about the center of mass.
- Therefore, the reason is also incorrect because the frictional force does provide the necessary torque for rolling.

### Conclusion
Both the assertion (A) and the reason (R) are false. Therefore, the correct answer is that both statements are incorrect.

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

---