A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizon be `30^(@)`, the angle of friction will be

Options

A. `3^(@)`
B. `60^(@)`
C. `45^(@)`
D. `15^(@)`

Answer

To solve the problem, we need to understand the relationship between the angle of inclination of the plane and the angle of friction when a body is on the verge of sliding down the inclined plane.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The angle of inclination of the plane (θ) = 30 degrees.
- The body is on the point of sliding down the inclined plane.

2. **Understand the Concept of Friction**:
- The angle of friction (φ) is defined as the angle between the normal force and the resultant force acting on the body. It is the angle at which the static friction force is equal to the component of gravitational force acting down the plane.

3. **Condition for Sliding**:
- A body will start to slide down an inclined plane when the component of gravitational force parallel to the incline exceeds the maximum static friction force.
- At the point of impending motion, the angle of inclination (θ) is equal to the angle of friction (φ).

4. **Apply the Condition**:
- Since the body is on the verge of sliding down, we can state that:
\[ θ = φ \]
- Given that θ = 30 degrees, we can substitute this into the equation.

5. **Conclusion**:
- Therefore, the angle of friction (φ) is also:
\[ φ = 30 \text{ degrees} \]

### Final Answer:
The angle of friction is **30 degrees**.