A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

Explanation

To solve the problem, we need to analyze the forces acting on the motorcycle as it ascends the overbridge. Let's break down the solution step by step.

### Step 1: Understand the Forces Acting on the Motorcycle
When the motorcycle is on the overbridge, there are three main forces acting on it:
1. The gravitational force (weight) acting downwards, \( F_g = mg \), where \( m \) is the mass of the motorcycle and \( g \) is the acceleration due to gravity.
2. The normal force (\( N \)) acting perpendicular to the surface of the bridge.
3. The centripetal force required to keep the motorcycle moving in a circular path, given by \( F_c = \frac{mv^2}{R} \), where \( v \) is the speed of the motorcycle and \( R \) is the radius of the bridge.

### Step 2: Draw the Free Body Diagram
As the motorcycle ascends, we can draw a free body diagram showing:
- The gravitational force acting downwards.
- The normal force acting perpendicular to the surface.
- The centripetal force acting towards the center of the circular path.

### Step 3: Resolve the Gravitational Force
The gravitational force can be resolved into two components:
- One component acting perpendicular to the surface of the bridge: \( mg \cos \theta \)
- Another component acting parallel to the surface of the bridge: \( mg \sin \theta \)

Here, \( \theta \) is the angle that the surface of the bridge makes with the horizontal.

### Step 4: Apply Newton's Second Law
For the motorcycle to maintain a circular motion while ascending, the forces must balance. The equation can be set up as follows:
\[ N + \frac{mv^2}{R} = mg \cos \theta \]
Where:
- \( N \) is the normal force.
- \( \frac{mv^2}{R} \) is the centripetal force.

### Step 5: Rearranging the Equation
From the equation above, we can isolate the normal force:
\[ N = mg \cos \theta - \frac{mv^2}{R} \]

### Step 6: Analyze the Behavior of Normal Force
As the motorcycle ascends from point A to point B:
- The angle \( \theta \) decreases, which means \( \cos \theta \) increases.
- Since \( mg \) and \( \frac{mv^2}{R} \) are constants (mass, speed, and radius are constant), the term \( mg \cos \theta \) will increase as \( \theta \) decreases.

### Step 7: Conclusion
Since \( N \) is directly proportional to \( \cos \theta \), and \( \cos \theta \) increases as the motorcycle ascends, it follows that the normal force \( N \) also increases.

Thus, the correct answer is that the normal force **increases** as the motorcycle ascends on the overbridge.

### Final Answer
The normal force on the motorcycle **increases** as it ascends on the overbridge.

---