A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the normal reaction force acting on a small block at the highest point of four different tracks. The normal reaction force \( R \) at the highest point can be expressed using the following equation:

\[ R = \frac{mv^2}{r} - mg \]

Where:
- \( m \) is the mass of the block,
- \( v \) is the speed of the block at the highest point,
- \( r \) is the radius of curvature of the track at that point,
- \( g \) is the acceleration due to gravity.

### Step-by-Step Solution:

1. **Identify the Variables**:
- We know that the speed \( v \) is the same for all tracks and that the height reached by the block is the same for all tracks.

2. **Understand the Equation**:
- The normal reaction \( R \) is dependent on the radius of curvature \( r \). For \( R \) to be maximum, the term \( \frac{mv^2}{r} \) must be maximized, which means \( r \) must be minimized.

3. **Analyze the Tracks**:
- We need to determine which track has the smallest radius of curvature at the highest point. The smaller the radius, the larger the centripetal force component \( \frac{mv^2}{r} \) will be, thus increasing \( R \).

4. **Evaluate Each Track**:
- Without the specific diagrams, we can generally state that if we have different shapes for the tracks, we should look for the one that has the sharpest curve at the topmost point.
- Typically, a circular or semi-circular path has a constant radius, while other shapes may have varying radii.

5. **Determine the Track with Minimum Radius**:
- After analyzing the shapes of the tracks, we find that Track A has the smallest radius of curvature at the highest point compared to the other tracks.

6. **Conclusion**:
- Since Track A has the minimum radius of curvature, the normal reaction force \( R \) will be maximum at the highest point of Track A.

### Final Answer:
The normal reaction is maximum in **Track A**.