In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

Options

A. increase
B. decrease
C. remain the same
D. may increase or decrease

Answer

To solve the problem, we need to analyze the situation where the contact force by a rough horizontal surface on a body has a constant magnitude, and the angle between this force and the vertical is decreased. We will explore how this affects the frictional force between the surface and the body.

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
- The contact force \( F_C \) acts at an angle \( \theta \) with the vertical.
- The normal force \( N \) acts perpendicular to the surface.
- The frictional force \( F_f \) acts parallel to the surface.

2. **Identify the Components of the Contact Force**:
- The contact force can be resolved into two components:
- Vertical component: \( F_{C_y} = F_C \cos(\theta) \)
- Horizontal component: \( F_{C_x} = F_C \sin(\theta) \)

3. **Analyze the Normal Force**:
- The normal force \( N \) is affected by the vertical component of the contact force. Since the contact force is constant, the normal force can be expressed as:
\[ N = mg - F_{C_y} = mg - F_C \cos(\theta) \]
- Here, \( mg \) is the weight of the body.

4. **Effect of Decreasing the Angle \( \theta \)**:
- As the angle \( \theta \) decreases, the vertical component \( F_{C_y} \) (which is \( F_C \cos(\theta) \)) increases because \( \cos(\theta) \) approaches 1.
- This results in a decrease in the normal force \( N \) because more of the contact force is acting vertically.

5. **Determine the Frictional Force**:
- The frictional force \( F_f \) is given by:
\[ F_f = \mu N \]
- Where \( \mu \) is the coefficient of friction. Since \( N \) decreases as \( \theta \) decreases, the frictional force \( F_f \) will also decrease.

6. **Conclusion**:
- Therefore, as the angle between the contact force and the vertical decreases, the frictional force between the surface and the body will **decrease**.

### Final Answer:
The frictional force between the surface and the body will **decrease**.