Step 1: Understanding the Concept:
When a vehicle moves on a curved surface, the net force towards the center of curvature provides the necessary centripetal force. The normal reaction $N$ varies depending on the direction of curvature relative to the weight of the vehicle.
Step 2: Key Formula or Approach:
1. Horizontal road: $N = mg$
2. Convex road (hill): $mg - N = \frac{mv^2}{r} \implies N = mg - \frac{mv^2}{r}$
3. Concave road (valley): $N - mg = \frac{mv^2}{r} \implies N = mg + \frac{mv^2}{r}$
Step 3: Detailed Explanation:
For a vehicle of mass $m$ and speed $v$:
On a horizontal road, the normal reaction simply balances the weight.
On a convex road, the normal force is reduced because a portion of the gravity is utilized to provide the downward centripetal force.
On a concave road, the normal force must push upward with enough strength to both balance the weight and provide the upward centripetal force.
Comparing the three: $mg + \frac{mv^2}{r}>mg>mg - \frac{mv^2}{r}$.
Step 4: Final Answer:
The normal reaction is maximum on the concave road surface.