The angle of banking is independent of

Options

A. speed of vehicle
B. radius of cuvature of road
C. height of inclination
D. None of these

Explanation

To solve the question regarding the angle of banking and its independence from certain parameters, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Banking**:
- Banking of a road is designed to help vehicles negotiate curves without skidding. The angle of banking (θ) allows the vehicle to maintain a certain speed while turning.

2. **Identifying Forces Acting on the Vehicle**:
- When a vehicle is on a banked road, two main forces act on it:
- The gravitational force (mg) acting downwards.
- The normal force (N) acting perpendicular to the surface of the road.

3. **Breaking Down the Forces**:
- The normal force can be resolved into two components:
- \( N \cos(\theta) \) acting vertically (balancing the weight).
- \( N \sin(\theta) \) acting horizontally (providing the centripetal force).

4. **Setting Up the Equations**:
- The vertical forces balance gives us:
\[ N \cos(\theta) = mg \]
- The horizontal forces provide the centripetal force required for circular motion:
\[ N \sin(\theta) = \frac{mv^2}{r} \]

5. **Dividing the Equations**:
- Dividing the second equation by the first:
\[ \frac{N \sin(\theta)}{N \cos(\theta)} = \frac{mv^2/r}{mg} \]
- This simplifies to:
\[ \tan(\theta) = \frac{v^2}{rg} \]

6. **Analyzing the Relationship**:
- From the equation \( \tan(\theta) = \frac{v^2}{rg} \), we can see that the angle of banking (θ) depends on:
- The speed of the vehicle (v)
- The radius of curvature (r)
- The acceleration due to gravity (g)

7. **Identifying the Independent Factor**:
- The angle of banking does not depend on the height of inclination of the road. Thus, among the options provided, the angle of banking is independent of the height of inclination.

### Conclusion:
- The correct answer is that the angle of banking is independent of the **height of inclination**.