The limiting value of static friction between two contact surfaces is

Options

A. Proportional to normal force between the surfaces in contact
B. Independent of area of contact
C. Depends on the microscopic area of constant magnitude
D. All of the above

Answer

To solve the question regarding the limiting value of static friction between two contact surfaces, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Static Friction**:
Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It acts when an external force is applied but does not exceed a certain limit.

2. **Limiting Value of Static Friction**:
The limiting value of static friction (F_s) can be expressed using the formula:
\[ F_s = \mu_s \cdot N \]
where:
- \( F_s \) is the limiting static friction force,
- \( \mu_s \) is the coefficient of static friction,
- \( N \) is the normal force acting on the object.

3. **Normal Force**:
The normal force (N) is typically equal to the weight of the object when it is resting on a horizontal surface. For an object of mass \( m \), the normal force can be calculated as:
\[ N = m \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

4. **Combining the Equations**:
Substituting the expression for normal force into the static friction equation gives:
\[ F_s = \mu_s \cdot (m \cdot g) \]

5. **Conclusion**:
The limiting value of static friction depends on both the coefficient of static friction (\( \mu_s \)) and the normal force (\( N \)). Therefore, the limiting value of static friction is directly proportional to the normal force acting on the surfaces in contact.

### Final Answer:
The limiting value of static friction between two contact surfaces is given by:
\[ F_s = \mu_s \cdot N \]
where \( N \) is the normal force, and it is dependent on the mass of the body and the coefficient of static friction.

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