Two trains A and B are running in the same direction on the parallel rails such that A is faster than B. Packets of equal weight are transfcrred from A to B. What will happen due to this :

Options

A. A will be accelerated but B will be retarded.
B. B will be accelerated but A will be retarded
C. there will be no change in A but B will accelerated.
D. there will be no change in B, but A will be accelerated

Explanation

To solve the problem, we need to analyze the situation involving two trains, A and B, moving in the same direction, where train A is faster than train B. We will also consider the effect of transferring packets of equal weight from train A to train B.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- Let the speed of train A be \( V_A \) and the speed of train B be \( V_B \).
- Given that \( V_A > V_B \), train A is moving faster than train B.

2. **Momentum Consideration**:
- The momentum of an object is given by the product of its mass and velocity. For train A, the momentum is \( P_A = m_A \cdot V_A \), and for train B, it is \( P_B = m_B \cdot V_B \).
- When packets of equal weight are transferred from A to B, the mass of train A decreases while the mass of train B increases.

3. **Effect on Train A**:
- As packets are transferred from train A to train B, the mass \( m_A \) of train A decreases. Since the velocity \( V_A \) remains the same initially, the momentum \( P_A \) of train A decreases.
- According to Newton's second law, a decrease in momentum over time implies that the acceleration of train A is negative (retardation).

4. **Effect on Train B**:
- Conversely, as packets are added to train B, its mass \( m_B \) increases. The velocity \( V_B \) remains the same initially, but the momentum \( P_B \) of train B increases.
- An increase in momentum over time indicates that the acceleration of train B is positive (acceleration).

5. **Conclusion**:
- Therefore, as packets are transferred from A to B, train A will experience a decrease in momentum leading to retardation, while train B will experience an increase in momentum leading to acceleration.
- The correct option is that train B will be accelerated and train A will be retarded.

### Final Answer:
**B will be accelerated and A will be retarded.**

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