A car runs east to west and another car B of the same mass runs from west to east at the same path along the equator. A presses the track with a force `N_(1)` and B presses the track with a force `N_(2)`. Then

Options

A. `N_1gtN_2`
B. `N_1ltN_2`
C. `N_1=N_2`
D. the information is insufficient to find the relation between `N_1 and N_2`.

Answer

To solve the problem, we need to analyze the forces acting on both cars A and B as they move along the equator of the Earth. Both cars have the same mass and are moving in opposite directions.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- Car A moves from east to west, while car B moves from west to east. Both are moving along the equator of the Earth.

2. **Identifying Forces**:
- Each car experiences gravitational force downward, which is \( mg \), where \( m \) is the mass of the car and \( g \) is the acceleration due to gravity.
- Each car also experiences a centrifugal force due to the Earth's rotation, which acts outward (upward) and is given by \( \frac{mv^2}{R} \), where \( v \) is the velocity of the car relative to the Earth's rotation and \( R \) is the radius of the Earth.

3. **Calculating the Velocities**:
- For car A (moving against the rotation of Earth):
\[ v_A = \omega R - v \]
- For car B (moving with the rotation of Earth):
\[ v_B = \omega R + v \]
- Here, \( \omega \) is the angular velocity of the Earth.

4. **Comparing Velocities**:
- Since \( v_B \) includes an additional \( v \) compared to \( v_A \), we conclude:
\[ v_B > v_A \]

5. **Setting Up the Equations for Normal Force**:
- For car A, the normal force \( N_1 \) is given by:
\[ N_1 + \frac{mv_A^2}{R} = mg \]
Rearranging gives:
\[ N_1 = mg - \frac{mv_A^2}{R} \]
- For car B, the normal force \( N_2 \) is given by:
\[ N_2 + \frac{mv_B^2}{R} = mg \]
Rearranging gives:
\[ N_2 = mg - \frac{mv_B^2}{R} \]

6. **Comparing Normal Forces**:
- Since \( v_B > v_A \), it follows that:
\[ \frac{mv_B^2}{R} > \frac{mv_A^2}{R} \]
- Therefore, substituting back into the equations for \( N_1 \) and \( N_2 \):
\[ N_2 < N_1 \]
- Thus, we conclude that:
\[ N_1 > N_2 \]

7. **Final Conclusion**:
- The correct answer is that the normal force exerted by car A on the track is greater than that exerted by car B:
\[ N_1 > N_2 \]