A vehicle is moving on a track as shown in Fig. The normal reaction between tyre's and road is :

Options

A. maximum at A
B. maximum at B
C. maximum at C
D. same at A, B and C

Answer

To solve the problem of determining the normal reaction between the tires and the road as the vehicle moves along the track, we can follow these steps:

### Step 1: Analyze the Vehicle's Motion
The vehicle is moving along a track that has inclines and declines. We need to consider the forces acting on the vehicle at different points on the track, particularly at points B and C where the incline is more pronounced.

**Hint:** Identify the points of interest on the track where the incline changes significantly.

### Step 2: Identify Forces Acting on the Vehicle
At any point on the track, the forces acting on the vehicle include:
- The weight of the vehicle (acting downwards, \( W = mg \))
- The normal force (acting perpendicular to the road surface)

**Hint:** Remember that the normal force adjusts based on the incline of the road and the weight of the vehicle.

### Step 3: Analyze the Normal Force at Point B
At point B, where the incline is steep, the normal force will be affected by both the weight of the vehicle and the centripetal force required for the vehicle to navigate the curve. The vehicle experiences maximum stress here due to the steep incline.

**Hint:** Consider how the angle of incline affects the distribution of forces acting on the vehicle.

### Step 4: Calculate the Normal Force
The normal force can be calculated using the equation:
\[ N = mg \cos(\theta) + \frac{mv^2}{r} \]
where:
- \( N \) is the normal force,
- \( m \) is the mass of the vehicle,
- \( g \) is the acceleration due to gravity,
- \( \theta \) is the angle of incline at point B,
- \( v \) is the velocity of the vehicle,
- \( r \) is the radius of the curve.

At point B, the vehicle experiences the maximum normal force due to the combination of gravitational force and the centripetal force.

**Hint:** Make sure to account for both gravitational and centripetal forces when calculating the normal force.

### Step 5: Conclusion
After analyzing the forces and calculating the normal force at point B, we conclude that the normal reaction between the tires and the road is maximum at this point due to the steep incline and the vehicle's motion.

**Final Answer:** The normal reaction between the tires and the road is maximum at point B.