Assertion : Force of friction depends on the actual area of contact
Reason : Smoother the surfaces of contact smaller is opposition to motion .

Options

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

Explanation

To solve the assertion-reason question, we will analyze both the assertion and the reason separately.

### Step 1: Analyze the Assertion
The assertion states: "Force of friction depends on the actual area of contact."

- **Understanding Friction**: The force of friction (F_friction) is given by the equation:
\[ F_{\text{friction}} = \mu \cdot N \]
where \( \mu \) is the coefficient of friction and \( N \) is the normal force acting on the object.

- **Area of Contact**: It is important to note that the coefficient of friction \( \mu \) is determined by the nature of the surfaces in contact and does not depend on the area of contact. The total frictional force is independent of the area of contact, provided that the normal force remains constant.

- **Conclusion on Assertion**: Therefore, the assertion that "the force of friction depends on the actual area of contact" is **incorrect**.

### Step 2: Analyze the Reason
The reason states: "Smoother the surfaces of contact, smaller is the opposition to motion."

- **Understanding Smooth Surfaces**: When surfaces are smoother, the coefficient of friction \( \mu \) decreases. A smooth surface can have a coefficient of friction approaching zero, which means there is less resistance to motion.

- **Effect on Frictional Force**: Since the frictional force is directly proportional to the coefficient of friction, a smaller \( \mu \) results in a smaller frictional force. Thus, smoother surfaces indeed offer less opposition to motion.

- **Conclusion on Reason**: The reason that "smoother the surfaces of contact, smaller is the opposition to motion" is **correct**.

### Final Conclusion
- **Assertion**: Incorrect
- **Reason**: Correct

### Summary
The assertion is incorrect because the force of friction does not depend on the area of contact. The reason is correct as smoother surfaces lead to a lower coefficient of friction, resulting in less opposition to motion.