A curved road is banked for speed `v_(0)`. When a car moves along the road with a constant speed `v`, the force the friction between the road and the tyres is F. Which of the following statements(s) is (are) correct ?

Options

A. If `v=0,F=0`
B. If `v= lt v_(0),F` acts outwards
C. If `v gt v_(0), F` acts inwards
D. If `v=v_(0),F=0`

Answer

To solve the question regarding the banked road and the forces acting on a car moving at different speeds, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Banked Curve**:
- A banked road is designed to help vehicles navigate curves without relying solely on friction. The angle of the bank (θ) is determined for a specific speed \( v_0 \).

2. **Forces Acting on the Car**:
- When a car moves on a banked curve, the forces acting on it include:
- Gravitational force (mg) acting downwards.
- Normal force (N) acting perpendicular to the surface of the road.
- Frictional force (F) which can act either up or down the bank depending on the speed of the car.

3. **Case 1: When \( v = 0 \)**:
- If the car is at rest (v = 0), there is no centripetal force required. Therefore, the frictional force \( F = 0 \).
- **Conclusion**: Option 1 is incorrect.

4. **Case 2: When \( v < v_0 \)**:
- If the speed of the car is less than the banked speed \( v_0 \), the car tends to slide down the bank.
- In this case, friction acts upwards (against gravity) to keep the car from sliding down.
- **Conclusion**: Option 2 is correct.

5. **Case 3: When \( v > v_0 \)**:
- If the speed of the car is greater than \( v_0 \), the required centripetal force exceeds what is provided by the banking alone. The car tends to slide outward.
- Here, friction acts downwards (towards the center of the curve) to prevent the car from sliding off.
- **Conclusion**: Option 3 is correct.

6. **Case 4: When \( v = v_0 \)**:
- At the designed speed \( v_0 \), the forces are balanced. The gravitational component down the slope is equal to the required centripetal force, and thus, no friction is needed.
- **Conclusion**: Option 4 is correct.

### Final Summary of Options:
- Option 1: Incorrect (F = 0 when v = 0)
- Option 2: Correct (F acts upwards when v < v_0)
- Option 3: Correct (F acts downwards when v > v_0)
- Option 4: Correct (F = 0 when v = v_0)