Which of the statements below is correct?

Options

A. The angle of bank for a road is obtained from a consideration of the centripetal force required
B. There is no tendency for the vehicle to skid if a road is banked for the speed at which the vehicle is moving
C. The resultant force action on a vehicle will be that which maintains it in a circular path
D. All of the above statements are correct.

Explanation

To solve the question regarding the correctness of the statements about a banked road and vehicle motion, we can analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the First Statement**:
- The first statement claims that the angle of bank of the road is obtained from a consideration of centripetal force required.
- When a vehicle moves in a circular path, it requires a centripetal force to maintain that motion. This force can be provided by the horizontal component of the normal force acting on the vehicle when the road is banked.
- The angle of banking (θ) is determined by the relationship between the speed of the vehicle (v), the radius of the curve (R), and the acceleration due to gravity (g). The formula derived from the balance of forces gives us:
\[ \tan(\theta) = \frac{v^2}{gR} \]
- Therefore, this statement is **true**.

2. **Understanding the Second Statement**:
- The second statement asserts that there is no tendency for the vehicle to skid if the road is banked for the speed at which the vehicle is going.
- If the banking angle is correctly set for the speed of the vehicle, the horizontal component of the normal force will exactly provide the required centripetal force, resulting in no relative motion between the vehicle and the road. Hence, there will be no tendency to skid.
- Thus, this statement is also **true**.

3. **Understanding the Third Statement**:
- The third statement claims that the resultant force acting on the vehicle will be that which maintains it in a circular path.
- The forces acting on the vehicle are the weight (mg) acting downwards and the normal force (N) acting perpendicular to the surface. The net force providing the centripetal acceleration is the horizontal component of the normal force.
- The centripetal force required for circular motion is given by:
\[ F_c = \frac{mv^2}{R} \]
- The resultant force indeed maintains the vehicle in a circular path, confirming that this statement is also **true**.

4. **Conclusion**:
- Since all three statements are true, the correct answer to the question is that all statements are correct.

### Final Answer:
All statements are correct.

---